, . The spectrum of this operator consists of clusters of eigenvalues around the Landau levels. We
give asymptotic formulas for the rate of accumulation of eigenvalues in these clusters. When the compact is a Reinhardt domain we are able to show a more precise asymptotic formula.">
偶维外Landau-Neumann hamilton函数的特征值渐近性</gydF4y2Batitle>
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<p>在本页面</p><年代p一个nclass="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#abstract" aria-label="">抽象的</一个></年代p一个n><年代pan class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#introduction" aria-label="">介绍</一个></年代p一个n><年代pan class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#references" aria-label="">参考</一个></年代p一个n><年代pan class="sc-ePZHVD dxfCqj grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-bEjcJn JKlRH" href="#copyright" aria-label="">版权</一个></年代p一个n></d我v>
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<p class="sc-gmeYpB ctdkmR article_type">研究文章|<！-- -->开放获取</p><d我v class="sc-kZmsYB doGfnX article_citation">
体积<！-- -->
<!-- -->2009<！-- -->
<span class="sc-iSDuPN ezntTT">|</年代p一个n>文章的ID<！-- -->
<!-- -->873704<！-- -->
<span class="sc-iSDuPN ezntTT">|</年代p一个n><一个class="sc-htpNat bUhGXt link sc-fZwumE dqIsrA" href="https://doi.org/10.1155/2009/873704" aria-label="Doi-link">https://doi.org/10.1155/2009/873704</一个></d我v>
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<p>Mikael Persson.<！-- -->，<！-- -->
<!-- -->＂<年代p一个nclass="adjust-article-svg-size">偶维外Landau-Neumann hamilton函数的特征值渐近性</年代p一个n>＂，<！-- --><i>数学物理进展</我>，<！-- -->
<!-- -->卷。<！-- -->2009<！-- -->，<！-- -->
<!-- -->文章的ID<！-- -->873704<！-- -->，<！-- -->
<!-- -->15<！-- -->
<!-- -->
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<!-- -->2009<！-- -->。<！-- -->
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<h1 class="sc-iRbamj jZOxOO sc-RcBXQ kZecej article_title adjust-article-svg-size heading-title">偶维外Landau-Neumann hamilton函数的特征值渐近性</gydF4y2Bah1>
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<span class=""><b>Mikael Persson.</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-jrIrqw eeUyzW icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><sup>1</年代up></span>
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<p><sup>1</年代up><span>查尔默斯理工大学数学科学系，Göteborg大学，412 96 Göteborg，瑞典</年代p一个n></p></d我v>
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<b>学术编辑器:</gydF4y2Bab>帕维尔报告》</d我v>
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<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2008年6月27日</年代p一个n></d我v>
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<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2008年10月22日</年代p一个n></d我v>
<div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished">
<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</年代p一个n><年代p一个nclass="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2008年11月25日</年代p一个n></d我v>
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<article class="sc-jeCdPy jsyicZ article_body ">
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<h4 class="header" id="abstract">抽象的</gydF4y2Bah4>
<p>研究了中紧致域外具有恒定磁场的Schrödinger算符<年代vg height="13.775" id="M1" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="12.3" id="M2" style="vertical-align:-1.29163pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 12.3" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.3)">
<g transform="translate(72,-62.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。该操作员的频谱由地兰水平周围的特征值簇组成。我们为这些集群中的特征值积累的速率提供渐近式。当紧凑型是Reinhardt域时，我们能够显示更精确的渐近式。</p><年代p一个nclass="end-abs"></span>
<h4 id="introduction">1.介绍</gydF4y2Bah4>
<p>Landau Hamiltonian描述了一种在平面中移动的带电粒子，受到恒定磁场强度的影响<年代vg height="11.0625" id="M3" style="vertical-align:-0.30096pt;width:38.200001px;" version="1.1" viewbox="0 0 38.200001 11.0625" width="38.200001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.165419" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.205809" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>正交于平面。这是一个经典的结果，参见[<一个href="#B3">1</一个>，<一个href="#B6">2</一个>］，Landau Hamiltonian的光谱由无限的简并的特征值组成<年代vg height="13.55" id="M4" style="vertical-align:-2.29482pt;width:61.849998px;" version="1.1" viewbox="0 0 61.849998 13.55" width="61.849998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.7020884" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.865587" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.117086" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.619127" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.959347" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.21085" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="13.55" id="M5" style="vertical-align:-2.29482pt;width:87.887497px;" version="1.1" viewbox="0 0 87.887497 13.55" width="87.887497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.481594" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.695347" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.946846" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.148094" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.399593" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.613342" y="0">
．..</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，称为朗道水平。</p><p>gydF4y2Ba在本文中，我们将在紧凑的障碍物之外研究偶数Landau Hamiltonian，在边界处施加磁性Numann条件。我们研究该运营商的动机主要来自论文[<一个href="#B5">3.</一个>，<一个href="#B10">4</一个>］．在飞机中的外部Landau Hamiltonian的光谱特性在[<一个href="#B5">3.</一个>），重点讨论了本征函数的性质。一个更定性的研究是在[<一个href="#B10">4</一个>］，其中作者在一个朗道水平周围定了一个区间，并描述该聚类中的特征值收敛到那个朗道水平的速度。它们只在平面上工作，并且只在狄利克雷边界条件下工作。本文的目的是当我们在边界上施加磁诺伊曼条件时，进行同样的定性描述。此外，我们不局限于平面，而是在任意的偶维欧几里德空间中工作。</p><p>gydF4y2Ba结果表明，两种边界条件的特征值都以相同的速度累积到朗道能级;看到定理<一个href="#thm3.2">3.2</一个>的细节。然而，在Neumann设置下，特征值只能从下面累积到朗道水平。在狄利克雷情况下，它们只从上面累积。</p><p>gydF4y2Ba应该提到的是，我们假设移除的紧凑型集没有孔，其边界是光滑的。这比[中的紧凑型条件更严格<一个href="#B10">4</一个>］．</p><p>gydF4y2Ba近年来，人们研究了朗道哈密顿量的几种不同的微扰;参见[<一个href="#B10">4</一个>- - - - - -<一个href="#B13">11</一个>］．它们都有一个共同的想法，那就是对一个谱渐近性已知的托普利兹型算子进行简化。我们也做这种还原。我们使用的方法是基于伪微分算子的理论和边界偏微分方程的方法，这是我们在上述任何一篇论文中都没有看到的。</p><p>gydF4y2Ba节<一个href="#sec2">2</一个>，我们定义了朗道哈密顿量，并给出了它的谱、特征空间和格林函数的一些辅助结果。</p><p>gydF4y2Ba我们开始部分<一个href="#sec3">3.</一个>通过定义具有磁诺伊曼边界条件的外朗道哈密顿量，给出并证明了主要定理(定理<一个href="#thm3.1">3.1</一个>和<一个href="#thm3.2">3.2</一个>）关于算子的谱渐近性。证明的主要部分，缩减步骤，是相当技术性的，因此移到节<一个href="#sec4">4</一个>。当简化步骤完成后，我们使用toeplitz型算子谱的渐近公式，如[<一个href="#B8">8</一个>，<一个href="#B4">10</一个>］，在定理中获得渐近式<一个href="#thm3.2">3.2</一个>。</p><p>gydF4y2Ba在高维情况下(<年代vg height="13.775" id="M6" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="11.0625" id="M7" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>)，我们也考虑紧致障碍为莱因哈特域的情况。我们使用来自[的一些想法<一个href="#B9">12</一个>］证明特征值更精确的渐近配方。这是在部分完成的<一个href="#sec5">5</一个>。</p><gydF4y2Bah4 id="the-landau-hamiltonian-in-ℝ2𝑑">2. Landau Hamiltonian<年代vg height="13.775" id="M8" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg></h4>
<p>我们表示<年代vg height="16.5375" id="M9" style="vertical-align:-2.21957pt;width:105.625px;" version="1.1" viewbox="0 0 105.625 16.5375" width="105.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5375)">
<g transform="translate(72,-58.77)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.543869" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.52,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.65,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.006001" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-1.77,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,8.29,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>一个点在<年代vg height="13.775" id="M10" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。让<年代vg height="11.0625" id="M11" style="vertical-align:-0.30096pt;width:38.200001px;" version="1.1" viewbox="0 0 38.200001 11.0625" width="38.200001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.165419" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.205809" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和表示<年代vg height="20.237499" id="M12" style="vertical-align:-0.0pt;width:13.9px;" version="1.1" viewbox="0 0 13.9 20.237499" width="13.9" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.2375)">
<g transform="translate(72,-55.81)">
<text transform="matrix(1,0,0,-1,-70.49,65.55)">
<tspan style="font-size: 8.75px; " x="0" y="0">
→</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-69.58,56.29)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>磁矢量势<年代p一个nclass="displayed-label" id="eq001"><span altimg="C:\WINDOWS\Temp\MMLIMG61441.png" baseline="18" class="displayed" height="44" id="M13" width="517"></span></span>它对应的是一个强度恒定的各向同性磁场<年代vg height="10.325" id="M14" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。Landau Hamiltonian<年代vg height="10.325" id="M15" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="13.775" id="M16" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>描述均匀磁场中的带电无自旋粒子。它是由<年代p一个nclass="displayed-label" id="eq002"><span altimg="C:\WINDOWS\Temp\MMLIMG61445.png" baseline="6" class="displayed" height="27" id="M17" width="101"></span></span>并且基本上是在集合上自伴随的<年代vg height="19.200001" id="M18" style="vertical-align:-4.35121pt;width:57.262501px;" version="1.1" viewbox="0 0 57.262501 19.200001" width="57.262501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.2)">
<g transform="translate(72,-56.64)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.56,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1" y="9.21">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.96,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.45,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.4,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在通常的希尔伯特空间<年代vg height="17.674999" id="M19" style="vertical-align:-3.13504pt;width:86.900002px;" version="1.1" viewbox="0 0 86.900002 17.674999" width="86.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.675)">
<g transform="translate(72,-57.86)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.928822" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.969212" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.12,57.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.25,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-16.74,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-6.69,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。为了<年代vg height="13.6125" id="M20" style="vertical-align:-2.34499pt;width:76.887497px;" version="1.1" viewbox="0 0 76.887497 13.6125" width="76.887497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3269978" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.367388" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.618887" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.832638" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.411137" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.624886" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.276482" y="0">
，</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们还引入了自伴随算子<年代p一个nclass="displayed-label" id="eq003"><span altimg="C:\WINDOWS\Temp\MMLIMG61449.png" baseline="21" class="displayed" height="51" id="M21" width="309"></span></span>在希尔伯特空间<年代vg height="19.725" id="M22" style="vertical-align:-4.77652pt;width:85.962502px;" version="1.1" viewbox="0 0 85.962502 19.725" width="85.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.725)">
<g transform="translate(72,-56.22)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.48,57.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.58,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.69,57.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-25.82,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-12.32,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-7.44,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。请注意,<年代vg height="21.125" id="M23" style="vertical-align:-5.97513pt;width:87.212502px;" version="1.1" viewbox="0 0 87.212502 21.125" width="87.212502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.125)">
<g transform="translate(72,-55.1)">
<text transform="matrix(1,0,0,-1,-71.95,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.928822" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.969212" y="0">
⊗</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.45,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.3199997">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.4045279" y="9.3199997">
＝</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="9.3996477" y="9.3199997">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-19.17,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-6.71,57.98)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代p一个nclass="displayed-label" id="eq004"><span altimg="C:\WINDOWS\Temp\MMLIMG61452.png" baseline="7" class="displayed" height="33" id="M24" width="492"></span></span></p>
<h5 id="subsec2.1">2.1。Landau水平</gydF4y2Bah5>
<p>每个二维朗道哈密顿量的谱<年代vg height="16.2875" id="M25" style="vertical-align:-4.77652pt;width:16.725px;" version="1.1" viewbox="0 0 16.725 16.2875" width="16.725" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2875)">
<g transform="translate(72,-58.97)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>由所谓的朗道能级，特征值组成<年代vg height="13.55" id="M26" style="vertical-align:-2.29482pt;width:61.849998px;" version="1.1" viewbox="0 0 61.849998 13.55" width="61.849998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.7020884" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.865587" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.117086" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.619127" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.959347" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.21085" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="13.6125" id="M27" style="vertical-align:-2.29482pt;width:141.175px;" version="1.1" viewbox="0 0 141.175 13.6125" width="141.175" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.1897049" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.230095" y="0">
ℕ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.433022" y="0">
∶</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.822056" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.862446" y="0">
｛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="57.863884" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.115387" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="69.316635" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.56813" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.781883" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="87.033386" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="92.247131" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="106.82563" y="0">
｝</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，每一个都有无限的多样性。让<年代vg height="17.725" id="M28" style="vertical-align:-3.24037pt;width:133.1125px;" version="1.1" viewbox="0 0 133.1125 17.725" width="133.1125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.725)">
<g transform="translate(72,-57.82)">
<text transform="matrix(1,0,0,-1,-71.74,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.677562" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.881451" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.42,57.98)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.55,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-5.32,57.98)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,0.35,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.6393328" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.667219" y="0">
ℕ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,28.76,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个多索引。我们表示<年代vg height="16.15" id="M29" style="vertical-align:-3.24037pt;width:119.1875px;" version="1.1" viewbox="0 0 119.1875 16.15" width="119.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.15)">
<g transform="translate(72,-59.08)">
<text transform="matrix(1,0,0,-1,-71.95,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.7006481" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.9148788" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.891313" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.931702" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-36.58,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.93,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
⋯</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.769163" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.121887" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,17.62,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>多索引的长度<年代vg height="12.1125" id="M30" style="vertical-align:-0.17555pt;width:9.4125004px;" version="1.1" viewbox="0 0 9.4125004 12.1125" width="9.4125004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.1125)">
<g transform="translate(72,-62.31)">
<text transform="matrix(1,0,0,-1,-71.74,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>同时设置<年代vg height="16.15" id="M31" style="vertical-align:-3.24037pt;width:94.112503px;" version="1.1" viewbox="0 0 94.112503 16.15" width="94.112503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.15)">
<g transform="translate(72,-59.08)">
<text transform="matrix(1,0,0,-1,-71.74,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.214231" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.453228" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.493616" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.81,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.94,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.238997" y="0">
⋯</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.904776" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-6.6,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-0.92,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
！</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。从(<一个href="#eq004">2.4</一个>）它遵循的是<年代vg height="10.325" id="M32" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>由无穷退化的特征值组成<年代p一个nclass="displayed-label" id="eq005"><span altimg="C:\WINDOWS\Temp\MMLIMG61461.png" baseline="25" class="displayed" height="59" id="M33" width="229"></span></span>请注意,<年代vg height="19.387501" id="M34" style="vertical-align:-7.17903pt;width:64.150002px;" version="1.1" viewbox="0 0 64.150002 19.387501" width="64.150002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.3875)">
<g transform="translate(72,-56.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.52)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9899998" y="5.0900002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.7774487" y="5.0900002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.18" y="-7.1054274e-015">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.207886" y="-7.1054274e-015">
λ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.200001" y="6.98">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.99995" y="6.98">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-23.53,63.79)">
<tspan style="font-size: 6.25px; " x="0" y="0">
′</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如果<年代vg height="16.9625" id="M35" style="vertical-align:-2.21957pt;width:54.924999px;" version="1.1" viewbox="0 0 54.924999 16.9625" width="54.924999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.9625)">
<g transform="translate(72,-58.43)">
<text transform="matrix(1,0,0,-1,-71.95,60.7)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.7006481" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.9148788" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.891313" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.931702" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.644854" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.444805" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.08,67.01)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.61,60.7)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。因此有了<年代vg height="10.325" id="M36" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>由这种形式的特征值组成<年代vg height="16.6" id="M37" style="vertical-align:-4.74141pt;width:102.35px;" version="1.1" viewbox="0 0 102.35 16.6" width="102.35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.17,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.87,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.729975" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.893473" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.144974" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.534966" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.887691" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.539288" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="13.325" id="M38" style="vertical-align:-2.29482pt;width:39.9375px;" version="1.1" viewbox="0 0 39.9375 13.325" width="39.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.325)">
<g transform="translate(72,-61.34)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">
ℕ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><gydF4y2Bah5 id="subsec2.2">２．2.创造和湮灭算符</gydF4y2Bah5>
<p>eIgenspaces的结构<年代vg height="10.325" id="M39" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>已经在[<一个href="#B8">8</一个>］．我们给出的结果没有证明。引入复数符号是很方便的。让<年代vg height="16.6625" id="M40" style="vertical-align:-2.21957pt;width:135.27499px;" version="1.1" viewbox="0 0 135.27499 16.6625" width="135.27499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6625)">
<g transform="translate(72,-58.67)">
<text transform="matrix(1,0,0,-1,-71.95,60.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7023277" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.742718" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.906216" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.8,65.94)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.92,60.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.993498" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-3.68,65.94)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,2,60.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.6268301" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.667219" y="0">
ℂ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,30.49,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>， 在哪里<年代vg height="14.4125" id="M41" style="vertical-align:-0.51414pt;width:106.8625px;" version="1.1" viewbox="0 0 106.8625 14.4125" width="106.8625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.4125)">
<g transform="translate(72,-60.47)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.71,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.81,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.9,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="7.7805281" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="13.775648" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-17.47,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.228654" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,4.64,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。此外，我们使用标量势<年代vg height="16.75" id="M42" style="vertical-align:-2.21957pt;width:116.3375px;" version="1.1" viewbox="0 0 116.3375 16.75" width="116.3375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.75)">
<g transform="translate(72,-58.6)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.452748" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.855244" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.482075" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.522465" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="50.087017" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="54.250519" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.952606" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="66.428436" y="0">
4</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="72.679939" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.843437" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="79.34404" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="85.583038" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,16.14,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>复导数<年代p一个nclass="displayed-label" id="eq006"><span altimg="C:\WINDOWS\Temp\MMLIMG61471.png" baseline="20" class="displayed" height="47" id="M43" width="460"></span></span></p>
<p>我们定义创造和湮灭算符<年代vg height="18.1875" id="M44" style="vertical-align:-5.12378pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 18.1875" width="17.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.1875)">
<g transform="translate(72,-57.45)">
<text transform="matrix(1,0,0,-1,-71.95,62.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.3,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="8.6899996">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="16.700001" id="M45" style="vertical-align:-4.77652pt;width:16.475px;" version="1.1" viewbox="0 0 16.475 16.700001" width="16.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.7)">
<g transform="translate(72,-58.64)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.3,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代p一个nclass="displayed-label" id="eq007"><span altimg="C:\WINDOWS\Temp\MMLIMG62886.png" baseline="20" class="displayed" height="47" id="M46" width="355"></span></span>和注意,<年代p一个nclass="displayed-label" id="eq008"><span altimg="C:\WINDOWS\Temp\MMLIMG61475.png" baseline="12" class="displayed" height="33" id="M47" width="364"></span></span>的符号<年代vg height="18.1875" id="M48" style="vertical-align:-5.12378pt;width:17.2875px;" version="1.1" viewbox="0 0 17.2875 18.1875" width="17.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.1875)">
<g transform="translate(72,-57.45)">
<text transform="matrix(1,0,0,-1,-71.95,62.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.3,67.83)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="8.6899996">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>因为创建操作符的动机是它是的形式伴随<年代vg height="16.700001" id="M49" style="vertical-align:-4.77652pt;width:16.475px;" version="1.1" viewbox="0 0 16.475 16.700001" width="16.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.7)">
<g transform="translate(72,-58.64)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.3,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="11.1" id="M50" style="vertical-align:-0.1881pt;width:15.7125px;" version="1.1" viewbox="0 0 15.7125 11.1" width="15.7125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba一个函数<年代vg height="7.1624999" id="M51" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于最低的朗道级别<年代vg height="14.725" id="M52" style="vertical-align:-3.25793pt;width:17.1875px;" version="1.1" viewbox="0 0 17.1875 14.725" width="17.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.725)">
<g transform="translate(72,-60.22)">
<text transform="matrix(1,0,0,-1,-71.95,63.52)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.17,60.4)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如果并且只有<年代vg height="16.700001" id="M53" style="vertical-align:-4.77652pt;width:51.087502px;" version="1.1" viewbox="0 0 51.087502 16.700001" width="51.087502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.7)">
<g transform="translate(72,-58.64)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.3,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.87,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3897533" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.430141" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>为<年代vg height="13.6125" id="M54" style="vertical-align:-2.34499pt;width:73.912498px;" version="1.1" viewbox="0 0 73.912498 13.6125" width="73.912498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6125)">
<g transform="translate(72,-61.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3269978" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.367388" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.618887" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.832638" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.411137" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.624886" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。这意味着该功能<年代vg height="16.4375" id="M55" style="vertical-align:-2.34499pt;width:63.150002px;" version="1.1" viewbox="0 0 63.150002 16.4375" width="63.150002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.4375)">
<g transform="translate(72,-58.85)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-43.94,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-27.46,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个完整的函数，通过乘以<年代vg height="13.6875" id="M56" style="vertical-align:-0.13794pt;width:27.674999px;" version="1.1" viewbox="0 0 27.674999 13.6875" width="27.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6875)">
<g transform="translate(72,-61.05)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-66.39,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>特征空间<年代vg height="17.612499" id="M57" style="vertical-align:-5.41734pt;width:27.737499px;" version="1.1" viewbox="0 0 27.737499 17.612499" width="27.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.6125)">
<g transform="translate(72,-57.91)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.98,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>对应于<年代vg height="14.725" id="M58" style="vertical-align:-3.25793pt;width:17.1875px;" version="1.1" viewbox="0 0 17.1875 14.725" width="17.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.725)">
<g transform="translate(72,-60.22)">
<text transform="matrix(1,0,0,-1,-71.95,63.52)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.17,60.4)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>等同于福克空间</p><p><年代p一个nclass="displayed-label" id="eq009"><span altimg="C:\WINDOWS\Temp\MMLIMG61487.png" baseline="28" class="displayed" height="71" id="M59" width="441"></span></span>在这里,和其他地方,<年代vg height="10.95" id="M60" style="vertical-align:-0.12538pt;width:19.0375px;" version="1.1" viewbox="0 0 19.0375 10.95" width="19.0375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示勒贝格测度。一个函数<年代vg height="7.1624999" id="M61" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于特征空间<年代vg height="18.9375" id="M62" style="vertical-align:-6.47697pt;width:28.6px;" version="1.1" viewbox="0 0 28.6 18.9375" width="28.6" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.98,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>朗道级别的<年代vg height="16.5625" id="M63" style="vertical-align:-4.74141pt;width:18.387501px;" version="1.1" viewbox="0 0 18.387501 16.5625" width="18.387501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5625)">
<g transform="translate(72,-58.75)">
<text transform="matrix(1,0,0,-1,-71.95,63.52)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.17,60.4)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如果并且只有它可以用形式编写<年代p一个nclass="displayed-label" id="eq0010"><span altimg="C:\WINDOWS\Temp\MMLIMG61492.png" baseline="21" class="displayed" height="51" id="M64" width="198"></span></span>在哪里<年代vg height="24.725" id="M65" style="vertical-align:-4.04408pt;width:156.58749px;" version="1.1" viewbox="0 0 156.58749 24.725" width="156.58749" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,24.725)">
<g transform="translate(72,-52.22)">
<text transform="matrix(1,0,0,-1,-71.95,56.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.13,61.52)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∗</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.06,56.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.3800001" y="-6.0599999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.167449" y="-6.0599999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.56" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.587887" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.751385" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-13.64,61.52)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-8.57,56.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-4.4,61.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,0.79,59.28)">
<tspan style="font-size: 6.25px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,7,56.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⋯</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.653276" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.816774" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,33.48,61.52)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∗</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.1499996">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,39.16,56.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,43.32,62.36)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,48.52,60.17)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="16.924999" id="M66" style="vertical-align:-5.27927pt;width:18.700001px;" version="1.1" viewbox="0 0 18.700001 16.924999" width="18.700001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.925)">
<g transform="translate(72,-58.46)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.1500001" y="5.0900002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.9499521" y="5.0900002">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>都属于<年代vg height="18.7875" id="M67" style="vertical-align:-3.80708pt;width:23.1625px;" version="1.1" viewbox="0 0 23.1625 18.7875" width="23.1625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.7875)">
<g transform="translate(72,-56.97)">
<text transform="matrix(1,0,0,-1,-71.95,60.81)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℱ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.46,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.0100002">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。每个特征值的多重性<年代vg height="16.5625" id="M68" style="vertical-align:-4.74141pt;width:18.387501px;" version="1.1" viewbox="0 0 18.387501 16.5625" width="18.387501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5625)">
<g transform="translate(72,-58.75)">
<text transform="matrix(1,0,0,-1,-71.95,63.52)">
<tspan style="font-size: 12.50px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.17,60.4)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是无限的。我们表示<年代vg height="22.8125" id="M69" style="vertical-align:-9.76868pt;width:32.549999px;" version="1.1" viewbox="0 0 32.549999 22.8125" width="32.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,22.8125)">
<g transform="translate(72,-53.75)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.57,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.22,53.8)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="18.9375" id="M70" style="vertical-align:-6.47697pt;width:28.025px;" version="1.1" viewbox="0 0 28.025 18.9375" width="28.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.57,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.43,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>投影到eIgenspaces上<年代vg height="22.8125" id="M71" style="vertical-align:-9.76868pt;width:33.112499px;" version="1.1" viewbox="0 0 33.112499 22.8125" width="33.112499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,22.8125)">
<g transform="translate(72,-53.75)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.77,53.8)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="18.9375" id="M72" style="vertical-align:-6.47697pt;width:28.6px;" version="1.1" viewbox="0 0 28.6 18.9375" width="28.6" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.98,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，并由(<一个href="#eq2.2">2.16</一个>）表示正交分解<年代p一个nclass="displayed-label" id="eq0011"><span altimg="C:\WINDOWS\Temp\MMLIMG61501.png" baseline="17" class="displayed" height="48" id="M73" width="246"></span></span>在<年代vg height="11.1" id="M74" style="vertical-align:-0.1881pt;width:15.7125px;" version="1.1" viewbox="0 0 15.7125 11.1" width="15.7125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><gydF4y2Bah5 id="subsec2.3">2.3。解决方案</gydF4y2Bah5>
<p>让<年代vg height="19.887501" id="M75" style="vertical-align:-4.74141pt;width:106.6625px;" version="1.1" viewbox="0 0 106.6625 19.887501" width="106.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8875)">
<g transform="translate(72,-56.09)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,57.74)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.33,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.191385" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.819176" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.159397" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.435902" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="52.562611" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,2.41,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>做…的解决者<年代vg height="10.325" id="M76" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="13.55" id="M77" style="vertical-align:-2.29482pt;width:35.174999px;" version="1.1" viewbox="0 0 35.174999 13.55" width="35.174999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7398367" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.780226" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。一个核的显式公式<年代vg height="16.6" id="M78" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的<年代vg height="16.237499" id="M79" style="vertical-align:-4.74141pt;width:17.799999px;" version="1.1" viewbox="0 0 17.799999 16.237499" width="17.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在[<一个href="#B5">3.</一个>］为了<年代vg height="10.875" id="M80" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。节<一个href="#subsec4.2">4.2</一个>，我们将使用的行为<年代vg height="16.6" id="M81" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>对角线附近<年代vg height="9.875" id="M82" style="vertical-align:-2.29482pt;width:35.862499px;" version="1.1" viewbox="0 0 35.862499 9.875" width="35.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，引理如下所示。<年代p一个nclass="statement" id="lem2.1"><span class="statement-title">引理2.1。</年代p一个n><我><年代vg height="16.237499" id="M83" style="vertical-align:-4.74141pt;width:17.799999px;" version="1.1" viewbox="0 0 17.799999 16.237499" width="17.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是带核的积分算子吗<年代vg height="16.6" id="M84" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在对角线上具有以下奇点：</我><年代p一个nclass="displayed-label" id="eq2.1"><span altimg="C:\WINDOWS\Temp\MMLIMG62162.png" baseline="96" class="displayed" height="201" id="M85" width="470"></span></span><i>作为<年代vg height="13.55" id="M86" style="vertical-align:-2.29482pt;width:76.550003px;" version="1.1" viewbox="0 0 76.550003 13.55" width="76.550003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.5006001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.152916" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.493137" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.694626" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.746555" y="0">
→</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="54.888168" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof1"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>内核<年代vg height="16.6" id="M87" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的<年代vg height="16.237499" id="M88" style="vertical-align:-4.74141pt;width:17.799999px;" version="1.1" viewbox="0 0 17.799999 16.237499" width="17.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.7,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>可以写成<年代p一个nclass="displayed-label" id="eq0012"><span altimg="C:\WINDOWS\Temp\MMLIMG61517.png" baseline="10" class="displayed" height="40" id="M89" width="276"></span></span>既然变量是两两分开的，我们有<年代p一个nclass="displayed-label" id="eq0013"><span altimg="C:\WINDOWS\Temp\MMLIMG61518.png" baseline="25" class="displayed" height="59" id="M90" width="356"></span></span>的公式<年代vg height="13.6875" id="M91" style="vertical-align:-0.13794pt;width:30.5px;" version="1.1" viewbox="0 0 30.5 13.6875" width="30.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.6875)">
<g transform="translate(72,-61.05)">
<text transform="matrix(1,0,0,-1,-71.95,61.23)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-66.39,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.19,64.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-50.89,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>给出于[<一个href="#B16">13</一个>］．它读了<年代p一个nclass="displayed-label" id="eq0014"><span altimg="C:\WINDOWS\Temp\MMLIMG61520.png" baseline="60" class="displayed" height="128" id="M92" width="477"></span></span>因此有<年代vg height="16.6" id="M93" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>就变成了<年代p一个nclass="displayed-label" id="eq2.2"><span altimg="C:\WINDOWS\Temp\MMLIMG61522.png" baseline="26" class="displayed" height="67" id="M94" width="507"></span></span>在哪里<年代p一个nclass="displayed-label" id="eq0015"><span altimg="C:\WINDOWS\Temp\MMLIMG61523.png" baseline="24" class="displayed" height="54" id="M95" width="417"></span></span>扩大<年代vg height="13.45" id="M96" style="vertical-align:-2.21957pt;width:24.9125px;" version="1.1" viewbox="0 0 24.9125 13.45" width="24.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.00144" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.164939" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.666259" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>显示,<年代p一个nclass="displayed-label" id="eq0016"><span altimg="C:\WINDOWS\Temp\MMLIMG62250.png" baseline="93" class="displayed" height="195" id="M97" width="453"></span></span>的(<一个href="#eq2.1">2.12</一个>）。</年代p一个n></p><h4 id="the-exterior-landau-neumann-hamiltonian-in-ℝ2𝑑">3.外朗道-诺依曼哈密顿函数<年代vg height="13.775" id="M98" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg></h4>
<p>让<年代vg height="14.1625" id="M99" style="vertical-align:-0.3135pt;width:55.662498px;" version="1.1" viewbox="0 0 55.662498 14.1625" width="55.662498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.1625)">
<g transform="translate(72,-60.67)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.990617" y="0">
⊂</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.57,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是具有光滑边界的单连通紧域<年代vg height="10.475" id="M100" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,让<年代vg height="17.237499" id="M101" style="vertical-align:-2.78387pt;width:83.662498px;" version="1.1" viewbox="0 0 83.662498 17.237499" width="83.662498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.2375)">
<g transform="translate(72,-58.21)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ω.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.765563" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.805952" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.8,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-24.96,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⧵</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3022318" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们定义外部Landau-Neumann Hamiltonian<年代vg height="14.2375" id="M102" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="14.775" id="M103" style="vertical-align:-3.13504pt;width:83.050003px;" version="1.1" viewbox="0 0 83.050003 14.775" width="83.050003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.775)">
<g transform="translate(72,-60.18)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.48,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-49,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.11,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-23.24,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ω.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.465731" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>通过<年代p一个nclass="displayed-label" id="eq3.1"><span altimg="C:\WINDOWS\Temp\MMLIMG62252.png" baseline="7" class="displayed" height="28" id="M104" width="166"></span></span>与磁性诺伊曼边界条件<年代p一个nclass="displayed-label" id="eq3.2"><span altimg="C:\WINDOWS\Temp\MMLIMG62845.png" baseline="7" class="displayed" height="23" id="M105" width="230"></span></span>在这里<年代vg height="7.2375002" id="M106" style="vertical-align:-0.11285pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 7.2375002" width="7.9749999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.2375)">
<g transform="translate(72,-66.21)">
<text transform="matrix(1,0,0,-1,-71.95,66.37)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示外部正常<年代vg height="10.475" id="M107" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们的目的是研究<年代vg height="14.2375" id="M108" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>不同于上一节讨论的Landau级别。下面的第一个定理表明<年代vg height="14.2375" id="M109" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>只能从下面累积到每个朗道水平。第二个定理说特征值确实从下面累积到朗道层，并给出了收敛速度。<年代p一个nclass="statement" id="thm3.1"><span class="statement-title">定理3.1。</年代p一个n><我>对于每一个<年代vg height="13.325" id="M110" style="vertical-align:-2.29482pt;width:39.9375px;" version="1.1" viewbox="0 0 39.9375 13.325" width="39.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.325)">
<g transform="translate(72,-61.34)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">
ℕ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和每个<年代vg height="7.1875" id="M111" style="vertical-align:-0.13794pt;width:7.6875px;" version="1.1" viewbox="0 0 7.6875 7.1875" width="7.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="11.0625" id="M112" style="vertical-align:-0.30096pt;width:74.099998px;" version="1.1" viewbox="0 0 74.099998 11.0625" width="74.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.282507" y="0">
<</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.322895" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.974491" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的特征值的个数<年代vg height="14.2375" id="M113" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在间隔内<年代vg height="16.6" id="M114" style="vertical-align:-4.74141pt;width:78.775002px;" version="1.1" viewbox="0 0 78.775002 16.6" width="78.775002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.18,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.19,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.59,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.391672" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是有限的。</我></年代p一个n></p>
<p>表示由<年代vg height="21.0375" id="M115" style="vertical-align:-4.72992pt;width:98.287498px;" version="1.1" viewbox="0 0 98.287498 21.0375" width="98.287498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.0375)">
<g transform="translate(72,-55.17)">
<text transform="matrix(1,0,0,-1,-71.95,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-67.72,66.03)">
<tspan style="font-size: 8.75px; " x="-0.25" y="10.82">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2356319" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-52.59,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-36.33,66.03)">
<tspan style="font-size: 8.75px; " x="-0.25" y="10.82">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2356319" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-21.2,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.115887" y="0">
⋯</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的特征值<年代vg height="14.2375" id="M116" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在间隔内<年代vg height="16.6" id="M117" style="vertical-align:-4.74141pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 16.6" width="66.525002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-42.81,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.99,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>并通过<年代vg height="13.45" id="M118" style="vertical-align:-2.21957pt;width:60.650002px;" version="1.1" viewbox="0 0 60.650002 13.45" width="60.650002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.640053" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.803552" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.080057" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.281305" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.157715" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.371468" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.248116" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>运营商的特征值数量<年代vg height="10.325" id="M119" style="vertical-align:-0.0pt;width:11.225px;" version="1.1" viewbox="0 0 11.225 10.325" width="11.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在间隔内<年代vg height="13.45" id="M120" style="vertical-align:-2.21957pt;width:32.237499px;" version="1.1" viewbox="0 0 32.237499 13.45" width="32.237499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.440005" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.641253" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.517662" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,计算多样性。同时,让<年代vg height="14.075" id="M121" style="vertical-align:-2.72116pt;width:47.625px;" version="1.1" viewbox="0 0 47.625 14.075" width="47.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.075)">
<g transform="translate(72,-60.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
C</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3395014" y="0">
一个</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.890833" y="0">
p</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.142332" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.305832" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.833118" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示的对数容量<年代vg height="10.325" id="M122" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>;参见[<一个href="#B7">14</一个>， 第2章]。<年代p一个nclass="statement" id="thm3.2"><span class="statement-title">定理3.2。</年代p一个n><我>让<年代vg height="13.325" id="M123" style="vertical-align:-2.29482pt;width:39.9375px;" version="1.1" viewbox="0 0 39.9375 13.325" width="39.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.325)">
<g transform="translate(72,-61.34)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.077658" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.118048" y="0">
ℕ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我><年代p一个nclass="list"><span class="list-item"><span class="list-label">(一)</年代p一个n><年代p一个nclass="list-content"><i>如果<年代vg height="10.875" id="M124" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>然后<年代vg height="25.725" id="M125" style="vertical-align:-5.84473pt;width:276.97501px;" version="1.1" viewbox="0 0 276.97501 25.725" width="276.97501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,25.725)">
<g transform="translate(72,-51.42)">
<text transform="matrix(1,0,0,-1,-71.95,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.9516678" y="0">
米</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.19,54.17)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.3824801" y="0">
→</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="14.948416" y="0">
∞</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-27.55,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.266163" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.429663" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,0.67,54.17)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,9.27,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,24.84,63.4)">
<tspan style="font-size: 8.75px; " x="-0.25" y="10.29">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,36.5,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,44.83,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,59.54,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.191385" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.893473" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.369307" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.620808" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.784306" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.947803" y="0">
C</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.287308" y="0">
一个</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.838638" y="0">
p</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.090137" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.253639" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.780922" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.94442" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,144.66,62.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></年代pan><span class="list-item"><span class="list-label">(b)</年代p一个n><年代p一个nclass="list-content"><i>如果<年代vg height="11.0625" id="M126" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>然后<年代vg height="19.9125" id="M127" style="vertical-align:-4.74141pt;width:347.48749px;" version="1.1" viewbox="0 0 347.48749 19.9125" width="347.48749" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.9125)">
<g transform="translate(72,-56.07)">
<text transform="matrix(1,0,0,-1,-71.95,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.640053" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.803552" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-48.37,57.72)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.17,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-18.18,57.72)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-9.58,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.104343" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.318094" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,22.59,57.72)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,29.6,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">
∼</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.843222" y="0">
（</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,59.69,65.7)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="15.981152" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="21.976273" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.6700001" y="9.2600002">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="10.326064" y="9.2600002">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="16.321184" y="9.2600002">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,88.13,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3269978" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.578498" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.054333" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.705929" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.944925" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.108425" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.271923" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.860523" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.336357" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.663357" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.427479" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.928078" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="70.491913" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="73.967751" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.307251" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="86.883347" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.359184" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.698685" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.46281" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.9634" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,200.27,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代vg height="13.125" id="M128" style="vertical-align:-1.95624pt;width:39.549999px;" version="1.1" viewbox="0 0 39.549999 13.125" width="39.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.125)">
<g transform="translate(72,-61.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.227454" y="0">
↘</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.281067" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></年代pan></span><i></i></span></p>
<h5 id="subsec3.1">3．1．定理的证明</gydF4y2Bah5>
<p>我们想要比较算子的频谱<年代vg height="10.325" id="M129" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M130" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然而,表达<年代vg height="14.2375" id="M131" style="vertical-align:-3.13504pt;width:48.674999px;" version="1.1" viewbox="0 0 48.674999 14.2375" width="48.674999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.62779" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.968012" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.12,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>没有任何意义<年代vg height="10.325" id="M132" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M133" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作用于不同的希尔伯特空间。我们引入希尔伯特空间<年代vg height="14.775" id="M134" style="vertical-align:-3.13504pt;width:84.400002px;" version="1.1" viewbox="0 0 84.400002 14.775" width="84.400002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.775)">
<g transform="translate(72,-60.18)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.48,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-48.14,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-27.25,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.38,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.690785" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>定义内部的朗道-诺依曼哈密顿量<年代vg height="14.2375" id="M135" style="vertical-align:-3.13504pt;width:21.025px;" version="1.1" viewbox="0 0 21.025 14.2375" width="21.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="14.775" id="M136" style="vertical-align:-3.13504pt;width:25.5375px;" version="1.1" viewbox="0 0 25.5375 14.775" width="25.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.775)">
<g transform="translate(72,-60.18)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.48,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>用()中的相同公式<一个href="#eq3.1">3.1</一个>）和(<一个href="#eq3.2">3.2</一个>），但与<年代vg height="10.6875" id="M137" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>取而代之<年代vg height="10.325" id="M138" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们注意到,<年代vg height="14.775" id="M139" style="vertical-align:-3.13504pt;width:104.9625px;" version="1.1" viewbox="0 0 104.9625 14.775" width="104.9625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.775)">
<g transform="translate(72,-60.18)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.928822" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.969212" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.51,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-20.86,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⊕</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.303192" y="0">
ℋ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,4.91,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和定义<年代vg height="15.025" id="M140" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代p一个nclass="displayed-label" id="eq0017"><span altimg="C:\WINDOWS\Temp\MMLIMG61569.png" baseline="7" class="displayed" height="28" id="M141" width="227"></span></span>逆<年代vg height="14.2375" id="M142" style="vertical-align:-3.13504pt;width:21.025px;" version="1.1" viewbox="0 0 21.025 14.2375" width="21.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>紧凑，所以<年代vg height="14.2375" id="M143" style="vertical-align:-3.13504pt;width:21.025px;" version="1.1" viewbox="0 0 21.025 14.2375" width="21.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在每个间隔中最多有一个有限数量的特征值<年代vg height="16.6" id="M144" style="vertical-align:-4.74141pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 16.6" width="66.525002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-42.81,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.99,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。运营商<年代vg height="14.2375" id="M145" style="vertical-align:-3.13504pt;width:21.025px;" version="1.1" viewbox="0 0 21.025 14.2375" width="21.025" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M146" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的正交子空间<年代vg height="11.1" id="M147" style="vertical-align:-0.1881pt;width:15.7125px;" version="1.1" viewbox="0 0 15.7125 11.1" width="15.7125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,所以<年代vg height="18.924999" id="M148" style="vertical-align:-3.13504pt;width:146.6875px;" version="1.1" viewbox="0 0 146.6875 18.924999" width="146.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.925)">
<g transform="translate(72,-56.86)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="12.42" y="-2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.3267579" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.5" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.352123" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.978954" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.019344" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.358604" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.522102" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-11.57,56.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-3.7,60.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.9391651" y="0">
∪</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.46669" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.805952" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.969452" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,34.13,56.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,41.14,60.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。这意味着<年代vg height="15.025" id="M149" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>具有相同的光谱渐近症状<年代vg height="14.2375" id="M150" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在每一个时间间隔<年代vg height="16.6" id="M151" style="vertical-align:-4.74141pt;width:66.525002px;" version="1.1" viewbox="0 0 66.525002 16.6" width="66.525002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.01,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-42.81,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.99,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，证明定理中的命题就足够了<一个href="#thm3.1">3.1</一个>和<一个href="#thm3.2">3.2</一个>的运营商<年代vg height="15.025" id="M152" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>而不是<年代vg height="14.2375" id="M153" style="vertical-align:-3.13504pt;width:19.950001px;" version="1.1" viewbox="0 0 19.950001 14.2375" width="19.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba自未绑定的运营商<年代vg height="10.325" id="M154" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="15.025" id="M155" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有不同的领域，我们不能直接比较它们。但是，它们作用于同一个希尔伯特空间，所以我们可以比较它们的逆矩阵。让<年代p一个nclass="displayed-label" id="eq0018"><span altimg="C:\WINDOWS\Temp\MMLIMG61584.png" baseline="7" class="displayed" height="31" id="M156" width="304"></span></span>并设置<年代p一个nclass="displayed-label" id="eq0019"><span altimg="C:\WINDOWS\Temp\MMLIMG61585.png" baseline="14" class="displayed" height="32" id="M157" width="314"></span></span><span class="statement" id="lem3.3"><span class="statement-title">引理3.3。</年代p一个n><我><年代vg height="10.575" id="M158" style="vertical-align:-0.20064pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.575)">
<g transform="translate(72,-63.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是非负的，紧致的。</我></年代p一个n></p>
<p><span class="statement" id="proof2"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>参见<一个href="#subsec4.1">4.1</一个>。</年代p一个n></p><p>根据韦尔定理，的基本谱<年代vg height="10.325" id="M159" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 10.325" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="15.025" id="M160" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 15.025" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-69.52,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.4300001" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>一致。自<年代vg height="15.6625" id="M161" style="vertical-align:-0.51414pt;width:72.800003px;" version="1.1" viewbox="0 0 72.800003 15.6625" width="72.800003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.6625)">
<g transform="translate(72,-59.47)">
<text transform="matrix(1,0,0,-1,-69.52,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.4300001" y="2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.285551" y="2.54">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.325939" y="2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.353825" y="2.54">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.694046" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="12.3" id="M162" style="vertical-align:-1.29163pt;width:36.3125px;" version="1.1" viewbox="0 0 36.3125 12.3" width="36.3125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.3)">
<g transform="translate(72,-62.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.652556" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.692945" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,定理<一个href="#thm3.1">3.1</一个>紧接于[<一个href="#B2">15</一个>，定理9.4.7]和这个事实<年代vg height="19.862499" id="M163" style="vertical-align:-4.74141pt;width:154.75px;" version="1.1" viewbox="0 0 154.75 19.862499" width="154.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8625)">
<g transform="translate(72,-56.11)">
<text transform="matrix(1,0,0,-1,-71.95,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.3267579" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.490257" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.742477" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.381809" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.422199" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-24.18,57.76)">
<tspan style="font-size: 8.75px; " x="0" y="0">
e</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.8858881" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="7.2904158" y="0">
年代</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-12.99,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.415719" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.042549" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.082939" y="0">
｛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.084377" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,34.88,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,45.75,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｝</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们继续定理的证明<一个href="#thm3.2">3.2</一个>。</p><p>gydF4y2Ba让<年代vg height="11.0625" id="M164" style="vertical-align:-0.30096pt;width:35.325001px;" version="1.1" viewbox="0 0 35.325001 11.0625" width="35.325001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8648672" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.905256" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是这样的,<年代vg height="19.862499" id="M165" style="vertical-align:-4.74141pt;width:291.26251px;" version="1.1" viewbox="0 0 291.26251 19.862499" width="291.26251" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8625)">
<g transform="translate(72,-56.11)">
<text transform="matrix(1,0,0,-1,-71.95,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3269978" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.85,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-41.2,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.591721" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.993258" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.207008" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-3.21,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,10.43,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.591721" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.993258" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.932423" y="0">
⧵</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="40.247158" y="0">
｛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.248596" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,65.47,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,76.34,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.00144" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.928102" y="0">
∩</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.46813" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,107.15,57.76)">
<tspan style="font-size: 8.75px; " x="0" y="0">
e</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="3.8858881" y="0">
年代</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="7.2904158" y="0">
年代</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,118.34,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.415719" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.055052" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.082939" y="0">
∅</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。表示特征值<年代vg height="16.237499" id="M166" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>通过<年代p一个nclass="displayed-label" id="eq0020"><span altimg="C:\WINDOWS\Temp\MMLIMG61595.png" baseline="9" class="displayed" height="30" id="M167" width="115"></span></span>和特征值<年代vg height="15.025" id="M168" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 15.025" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-69.52,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.4300001" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在间隔内<年代vg height="19.862499" id="M169" style="vertical-align:-4.74141pt;width:91.8125px;" version="1.1" viewbox="0 0 91.8125 19.862499" width="91.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8625)">
<g transform="translate(72,-56.11)">
<text transform="matrix(1,0,0,-1,-71.95,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.01,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-48.14,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.15,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-20.51,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.741756" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>通过<年代p一个nclass="displayed-label" id="eq0021"><span altimg="C:\WINDOWS\Temp\MMLIMG61598.png" baseline="9" class="displayed" height="30" id="M170" width="117"></span></span><span class="statement" id="lem3.4"><span class="statement-title">引理3.4。</年代p一个n><我>给予<年代vg height="12.8875" id="M171" style="vertical-align:-1.76814pt;width:38.799999px;" version="1.1" viewbox="0 0 38.799999 12.8875" width="38.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.8875)">
<g transform="translate(72,-61.69)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.5147829" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.555172" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.806671" y="0">
，</gydF4y2Batspan>
</text>
</g>
</g>
</svg>存在一个整数<年代vg height="10.725" id="M172" style="vertical-align:-0.1254pt;width:5.4124999px;" version="1.1" viewbox="0 0 5.4124999 10.725" width="5.4124999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.725)">
<g transform="translate(72,-63.42)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样</我><年代p一个nclass="displayed-label" id="eq0022"><span altimg="C:\WINDOWS\Temp\MMLIMG61601.png" baseline="13" class="displayed" height="34" id="M173" width="482"></span></span><i></i></span></p>
<p><span class="statement" id="proof3"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>看 [<一个href="#B10">4</一个>，命题2.2]。</年代p一个n></p><p>因此，研究了特征值的渐近学<年代vg height="15.025" id="M174" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 15.025" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-69.52,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.4300001" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>简化为研究toeplitz型算子的特征值<年代vg height="16.237499" id="M175" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。对于有界简单的连接集<年代vg height="10.5375" id="M176" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.5375)">
<g transform="translate(72,-63.57)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="13.775" id="M177" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，定义Toeplitz算子<年代vg height="19.512501" id="M178" style="vertical-align:-4.74141pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 19.512501" width="20.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.95,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代p一个nclass="displayed-label" id="eq0023"><span altimg="C:\WINDOWS\Temp\MMLIMG61607.png" baseline="14" class="displayed" height="35" id="M179" width="132"></span></span>在哪里<年代vg height="11.0625" id="M180" style="vertical-align:-3.24916pt;width:20.375px;" version="1.1" viewbox="0 0 20.375 11.0625" width="20.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.39,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示的特征函数<年代vg height="10.5375" id="M181" style="vertical-align:-0.16302pt;width:12.8625px;" version="1.1" viewbox="0 0 12.8625 10.5375" width="12.8625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.5375)">
<g transform="translate(72,-63.57)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。下面的引理将我们的问题简化为这些Toeplitz算子的研究，它们比<年代vg height="16.237499" id="M182" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。<年代p一个nclass="statement" id="lem3.5"><span class="statement-title">引理3.5。</年代p一个n><我>让<年代vg height="14.3875" id="M183" style="vertical-align:-3.25793pt;width:86.8125px;" version="1.1" viewbox="0 0 86.8125 14.3875" width="86.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.08,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⋐</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.031006" y="0">
⋐</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.071396" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-7.47,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是这样的紧域<年代vg height="14.5875" id="M184" style="vertical-align:-3.2316pt;width:81.150002px;" version="1.1" viewbox="0 0 81.150002 14.5875" width="81.150002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.5875)">
<g transform="translate(72,-60.33)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.3765302" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-56.03,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-50.04,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∩</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.527526" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.342621" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.383011" y="0">
∅</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。存在一个常数<年代vg height="11.0625" id="M185" style="vertical-align:-0.30096pt;width:37.8125px;" version="1.1" viewbox="0 0 37.8125 11.0625" width="37.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.852844" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.893232" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和子空间<年代vg height="11.25" id="M186" style="vertical-align:-0.3135pt;width:46.712502px;" version="1.1" viewbox="0 0 46.712502 11.25" width="46.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.25)">
<g transform="translate(72,-63)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.75306" y="0">
⊂</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.793449" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有限余维数</我><年代p一个nclass="displayed-label" id="eq3.3"><span altimg="C:\WINDOWS\Temp\MMLIMG61615.png" baseline="19" class="displayed" height="47" id="M187" width="321"></span></span><i>对所有<年代vg height="13.675" id="M188" style="vertical-align:-2.34499pt;width:39.799999px;" version="1.1" viewbox="0 0 39.799999 13.675" width="39.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.675)">
<g transform="translate(72,-61.06)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof4"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>参见<一个href="#subsec4.2">4.2</一个>。</年代p一个n></p><p>谱的渐近展开式<年代vg height="19.512501" id="M189" style="vertical-align:-4.74141pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 19.512501" width="20.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.95,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在下列引理中给出。<年代p一个nclass="statement" id="lem3.6"><span class="statement-title">引理3.6。</年代p一个n><我>表示由<年代vg height="21.0375" id="M190" style="vertical-align:-4.72992pt;width:101.475px;" version="1.1" viewbox="0 0 101.475 21.0375" width="101.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.0375)">
<g transform="translate(72,-55.17)">
<text transform="matrix(1,0,0,-1,-71.95,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-66.45,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="10.82">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-51.32,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.78,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="10.82">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-18.65,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.115887" y="0">
⋯</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的特征值<年代vg height="19.512501" id="M191" style="vertical-align:-4.74141pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 19.512501" width="20.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.95,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>并通过<年代vg height="19.512501" id="M192" style="vertical-align:-4.74141pt;width:54.0625px;" version="1.1" viewbox="0 0 54.0625 19.512501" width="54.0625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2139912" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.37749" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.141613" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.342861" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.6,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.97,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的特征值的个数<年代vg height="19.512501" id="M193" style="vertical-align:-4.74141pt;width:20.9125px;" version="1.1" viewbox="0 0 20.9125 19.512501" width="20.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.5125)">
<g transform="translate(72,-56.39)">
<text transform="matrix(1,0,0,-1,-71.95,61.17)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.95,66.24)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>大于<年代vg height="10.8125" id="M194" style="vertical-align:-0.20064pt;width:8.5749998px;" version="1.1" viewbox="0 0 8.5749998 10.8125" width="8.5749998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>(包括多重性)。然后</我><br><i></i><span class="list"><span class="list-item"><span class="list-label">(一)</年代p一个n><年代p一个nclass="list-content"><i>如果<年代vg height="10.875" id="M195" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们有<年代vg height="25.725" id="M196" style="vertical-align:-5.84473pt;width:228.75px;" version="1.1" viewbox="0 0 228.75 25.725" width="228.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,25.725)">
<g transform="translate(72,-51.42)">
<text transform="matrix(1,0,0,-1,-71.95,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">
我</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.9516678" y="0">
米</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.19,54.17)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.3824801" y="0">
→</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="14.948416" y="0">
∞</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.63,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.266163" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-8.86,63.4)">
<tspan style="font-size: 8.75px; " x="0" y="10.29">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,2.8,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,6.96,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,21.67,57.3)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.040389" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.203888" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.905975" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.381809" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.633308" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="38.79681" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="42.960308" y="0">
C</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.299809" y="0">
一个</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.851143" y="0">
p</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="63.102642" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="67.266144" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="76.080757" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.244255" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,106.08,62.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，</我></年代p一个n></年代pan><span class="list-item"><span class="list-label">(b)</年代p一个n><年代p一个nclass="list-content"><i>如果<年代vg height="11.0625" id="M197" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们有<年代vg height="19.9125" id="M198" style="vertical-align:-4.74141pt;width:269.28751px;" version="1.1" viewbox="0 0 269.28751 19.9125" width="269.28751" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.9125)">
<g transform="translate(72,-56.07)">
<text transform="matrix(1,0,0,-1,-71.95,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2139912" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.37749" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.141613" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.342861" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.6,65.92)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-0.87" y="8.1999998">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.97,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">
∼</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.843222" y="0">
（</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-2.88,65.7)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.329968" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="11.325088" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="15.981152" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="21.976273" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.6700001" y="9.2600002">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="10.326064" y="9.2600002">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="16.321184" y="9.2600002">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,25.56,60.85)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.3269978" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.578498" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.054333" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.705929" y="0">
！</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.944925" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.108425" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.271923" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="43.860523" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.336357" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.675858" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="62.439983" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="64.940582" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="70.491913" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="73.967751" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="82.307251" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="86.895851" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="90.371681" y="0">
n</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="98.698685" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="105.46281" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="107.9634" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,137.7,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代vg height="13.125" id="M199" style="vertical-align:-1.95624pt;width:39.549999px;" version="1.1" viewbox="0 0 39.549999 13.125" width="39.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.125)">
<g transform="translate(72,-61.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.227454" y="0">
↘</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.281067" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></年代pan></span><i></i></span></p>
<p><span class="statement" id="proof5"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>看 [<一个href="#B4">10</一个>第(a)部分和[引理3.2]<一个href="#B8">8</一个>［第(b)部分]。</年代p一个n></p><p><span class="statement" id="proof8"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>现在我们可以完成定理的证明了<一个href="#thm3.2">3.2</一个>。通过让<年代vg height="14.3875" id="M200" style="vertical-align:-3.25793pt;width:18.125px;" version="1.1" viewbox="0 0 18.125 14.3875" width="18.125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3875)">
<g transform="translate(72,-60.49)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.2375" id="M201" style="vertical-align:-3.13504pt;width:18.125px;" version="1.1" viewbox="0 0 18.125 14.2375" width="18.125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在引理<一个href="#lem3.5">3.5</一个>离我们的契约越来越近<年代vg height="10.325" id="M202" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们看到特征值<年代vg height="22.4375" id="M203" style="vertical-align:-5.84473pt;width:34.587502px;" version="1.1" viewbox="0 0 34.587502 22.4375" width="34.587502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,22.4375)">
<g transform="translate(72,-54.05)">
<text transform="matrix(1,0,0,-1,-71.95,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.00144" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.04,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="10.29">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-50.38,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｝</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的<年代vg height="16.237499" id="M204" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>满足<年代p一个nclass="displayed-label" id="eq3.4"><span altimg="C:\WINDOWS\Temp\MMLIMG61635.png" baseline="17" class="displayed" height="47" id="M205" width="231"></span></span>如果<年代vg height="10.875" id="M206" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代p一个nclass="displayed-label" id="eq3.5"><span altimg="C:\WINDOWS\Temp\MMLIMG61637.png" baseline="25" class="displayed" height="59" id="M207" width="400"></span></span>如果<年代vg height="11.0625" id="M208" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。因为公式(<一个href="#eq3.4">3．11</一个>）和(<一个href="#eq3.5">3.12</一个>）对指标的有限移位是敏感的，它遵循引理<一个href="#lem3.4">3.4</一个>的特征值<年代vg height="22.4375" id="M209" style="vertical-align:-5.84473pt;width:36.075001px;" version="1.1" viewbox="0 0 36.075001 22.4375" width="36.075001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,22.4375)">
<g transform="translate(72,-54.05)">
<text transform="matrix(1,0,0,-1,-71.95,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｛</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.00144" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.85,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="10.29">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.2443838" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-49.19,59.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
｝</gydF4y2Batspan>
</text>
</g>
</g>
</svg>
<svg height="15.025" id="M210" style="vertical-align:-0.0pt;width:11.6875px;" version="1.1" viewbox="0 0 11.6875 15.025" width="11.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-69.52,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-2.4300001" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>满足<年代p一个nclass="displayed-label" id="eq0024"><span altimg="C:\WINDOWS\Temp\MMLIMG61641.png" baseline="17" class="displayed" height="47" id="M211" width="302"></span></span>如果<年代vg height="10.875" id="M212" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代p一个nclass="displayed-label" id="eq0025"><span altimg="C:\WINDOWS\Temp\MMLIMG61643.png" baseline="27" class="displayed" height="63" id="M213" width="511"></span></span><br>如果我们把它转换成<年代vg height="15.025" id="M214" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们得到了<年代p一个nclass="displayed-label" id="eq0026"><span altimg="C:\WINDOWS\Temp\MMLIMG61645.png" baseline="17" class="displayed" height="47" id="M215" width="291"></span></span>为<年代vg height="10.875" id="M216" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代p一个nclass="displayed-label" id="eq0027"><span altimg="C:\WINDOWS\Temp\MMLIMG61647.png" baseline="71" class="displayed" height="149" id="M217" width="522"></span></span>为<年代vg height="11.0625" id="M218" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。这就完成了定理的证明<一个href="#thm3.2">3.2</一个>。</年代p一个n></p><h4 id="proof-of-the-lemmas">4.引理的证明</gydF4y2Bah4>
<p>在这一节，我们证明引理<一个href="#lem3.3">3.3.</一个>和<一个href="#lem3.5">3.5</一个>。我们将使用伪微分算子和边界层势的理论。有关这些工具的详情请参阅[<一个href="#B17">16</一个>］和[<一个href="#B1">17</一个>，第五章]。</p><gydF4y2Bah5 id="subsec4.1">4.1。引理的证明<一个href="#lem3.3">3.3.</一个></h5>
<p>运营商<年代vg height="10.325" id="M219" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="15.025" id="M220" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>都是由相同的表达式定义的，但是<年代vg height="15.025" id="M221" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>包含在<年代vg height="10.325" id="M222" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。它源自[<一个href="#B10">4</一个>，提案2.1]<年代vg height="16.625" id="M223" style="vertical-align:-1.29163pt;width:67.112503px;" version="1.1" viewbox="0 0 67.112503 16.625" width="67.112503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.625)">
<g transform="translate(72,-58.7)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="23.889999" y="-2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.62779" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.969999" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.297958" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="47.325844" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>， 因此<年代vg height="16.625" id="M224" style="vertical-align:-1.29163pt;width:96.487503px;" version="1.1" viewbox="0 0 96.487503 16.625" width="96.487503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.625)">
<g transform="translate(72,-58.7)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="25.129999" y="-2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.652556" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.700001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.727886" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="46.068108" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.796162" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="70.824043" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba接下来我们证明了紧凑的<年代vg height="10.575" id="M225" style="vertical-align:-0.20064pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.575)">
<g transform="translate(72,-63.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。让<年代vg height="13.4875" id="M226" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="9.9375" id="M227" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于<年代vg height="11.1" id="M228" style="vertical-align:-0.1881pt;width:15.7125px;" version="1.1" viewbox="0 0 15.7125 11.1" width="15.7125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。同时,让<年代vg height="13.4875" id="M229" style="vertical-align:-2.34499pt;width:49.037498px;" version="1.1" viewbox="0 0 49.037498 13.4875" width="49.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3897533" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.430141" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.682362" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="17.9375" id="M230" style="vertical-align:-2.34499pt;width:47.299999px;" version="1.1" viewbox="0 0 47.299999 17.9375" width="47.299999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.9375)">
<g transform="translate(72,-57.65)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="24.26" y="-2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7898493" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.84" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.09222" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然后<年代vg height="7.1624999" id="M231" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于……的领域<年代vg height="10.325" id="M232" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="7.4250002" id="M233" style="vertical-align:-0.11285pt;width:8.0375004px;" version="1.1" viewbox="0 0 8.0375004 7.4250002" width="8.0375004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.425)">
<g transform="translate(72,-66.06)">
<text transform="matrix(1,0,0,-1,-71.95,66.22)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于……的领域<年代vg height="15.025" id="M234" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 15.025" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.025)">
<g transform="translate(72,-59.98)">
<text transform="matrix(1,0,0,-1,-71.04,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.91000003" y="2.54">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,所以<年代vg height="13.7625" id="M235" style="vertical-align:-3.13504pt;width:81.9375px;" version="1.1" viewbox="0 0 81.9375 13.7625" width="81.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.7625)">
<g transform="translate(72,-60.99)">
<text transform="matrix(1,0,0,-1,-71.95,64.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7898493" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.830238" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-43.79,61.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.14,64.16)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⊕</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.303192" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-13.51,61.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<年代vg height="14.2375" id="M236" style="vertical-align:-3.13504pt;width:123.075px;" version="1.1" viewbox="0 0 123.075 14.2375" width="123.075" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.23,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-48.9,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.26,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⊕</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.303192" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-16.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-9.09,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-2.76,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,7.72,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。通过零件和使用（<一个href="#eq3.2">3.2</一个>）<gydF4y2Ba年代vg height="11.1875" id="M237" style="vertical-align:-3.13504pt;width:17.862499px;" version="1.1" viewbox="0 0 17.862499 11.1875" width="17.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1875)">
<g transform="translate(72,-63.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.22)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.62,63.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="11.1875" id="M238" style="vertical-align:-3.13504pt;width:16.799999px;" version="1.1" viewbox="0 0 16.799999 11.1875" width="16.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1875)">
<g transform="translate(72,-63.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.22)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.62,63.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,我们得到<年代p一个nclass="displayed-label" id="eq4.1"><span altimg="C:\WINDOWS\Temp\MMLIMG62840.png" baseline="57" class="displayed" height="120" id="M239" width="698"></span></span>在这里<年代vg height="10.95" id="M240" style="vertical-align:-0.1254pt;width:19.1875px;" version="1.1" viewbox="0 0 19.1875 10.95" width="19.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>表示表面测量上<年代vg height="10.475" id="M241" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba取一个平滑的截断函数<年代vg height="19.200001" id="M242" style="vertical-align:-4.35121pt;width:87.362503px;" version="1.1" viewbox="0 0 87.362503 19.200001" width="87.362503" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.2)">
<g transform="translate(72,-56.64)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.068275" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.48,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∞</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="-1.01" y="9.21">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.88,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-16.38,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-6.32,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样<年代vg height="13.85" id="M243" style="vertical-align:-2.53308pt;width:57.037498px;" version="1.1" viewbox="0 0 57.037498 13.85" width="57.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.85)">
<g transform="translate(72,-60.92)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.5520515" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.715551" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.592201" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.231533" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.271923" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在一个<年代vg height="10.325" id="M244" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然后我们可以替换<年代vg height="7.1624999" id="M245" style="vertical-align:-0.11285pt;width:7.5374999px;" version="1.1" viewbox="0 0 7.5374999 7.1624999" width="7.5374999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1625)">
<g transform="translate(72,-66.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="7.4250002" id="M246" style="vertical-align:-0.11285pt;width:8.0375004px;" version="1.1" viewbox="0 0 8.0375004 7.4250002" width="8.0375004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.425)">
<g transform="translate(72,-66.06)">
<text transform="matrix(1,0,0,-1,-71.95,66.22)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>通过<年代vg height="13.25" id="M247" style="vertical-align:-2.53308pt;width:45.037498px;" version="1.1" viewbox="0 0 45.037498 13.25" width="45.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.25)">
<g transform="translate(72,-61.4)">
<text transform="matrix(1,0,0,-1,-65.61,63.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.3390212" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.0507319" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.091121" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.655676" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="13.375" id="M248" style="vertical-align:-2.53308pt;width:46.037498px;" version="1.1" viewbox="0 0 46.037498 13.375" width="46.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.375)">
<g transform="translate(72,-61.3)">
<text transform="matrix(1,0,0,-1,-65.09,63.97)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.8600001" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.9298489" y="0.1">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.970238" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.534794" y="0.1">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在(的右边)<一个href="#eq4.1">4.1</一个>）.通过局部椭圆正则性我们得到<年代vg height="16.5375" id="M249" style="vertical-align:-2.21957pt;width:82.712502px;" version="1.1" viewbox="0 0 82.712502 16.5375" width="82.712502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5375)">
<g transform="translate(72,-58.77)">
<text transform="matrix(1,0,0,-1,-65.61,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.3390212" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.0507319" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.091121" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.47,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.6,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-20.09,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-10.04,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="17.237499" id="M250" style="vertical-align:-2.78387pt;width:107.5125px;" version="1.1" viewbox="0 0 107.5125 17.237499" width="107.5125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.2375)">
<g transform="translate(72,-58.21)">
<text transform="matrix(1,0,0,-1,-65.09,61.13)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.8600001" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.9298489" y="0.1">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.970238" y="0.1">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.07,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.2,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-19.69,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-6.86,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⧵</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3147354" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.653996" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然而,操作员<年代vg height="14.6" id="M251" style="vertical-align:-3.13504pt;width:67.175003px;" version="1.1" viewbox="0 0 67.175003 14.6" width="67.175003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-65.61,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.3390212" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.0507319" y="0">
↦</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.104343" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-41.11,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-26.04,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.3265181" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.400096" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-23.95,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>紧凑型是从什么角度考虑的<年代vg height="16.5375" id="M252" style="vertical-align:-2.21957pt;width:55.924999px;" version="1.1" viewbox="0 0 55.924999 16.5375" width="55.924999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.5375)">
<g transform="translate(72,-58.77)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.91,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.04,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-41.53,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.48,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>来<年代vg height="14.6" id="M253" style="vertical-align:-3.13504pt;width:36.862499px;" version="1.1" viewbox="0 0 36.862499 14.6" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>两者都是<年代vg height="16.0375" id="M254" style="vertical-align:-3.13504pt;width:58.025002px;" version="1.1" viewbox="0 0 58.025002 16.0375" width="58.025002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.0375)">
<g transform="translate(72,-59.17)">
<text transform="matrix(1,0,0,-1,-65.09,62.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.04" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.99" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.8600001" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.9298489" y="0.1">
↦</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.77,59.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.76,62.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.26,59.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="16.0375" id="M255" style="vertical-align:-3.13504pt;width:59.099998px;" version="1.1" viewbox="0 0 59.099998 16.0375" width="59.099998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.0375)">
<g transform="translate(72,-59.17)">
<text transform="matrix(1,0,0,-1,-65.09,62.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
̃</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.04" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.99" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-6.8600001" y="0.1">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.9298489" y="0.1">
↦</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.77,59.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.91,62.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-30.4,59.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>紧凑型从何而来<年代vg height="17.237499" id="M256" style="vertical-align:-2.78387pt;width:80.212502px;" version="1.1" viewbox="0 0 80.212502 17.237499" width="80.212502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.2375)">
<g transform="translate(72,-58.21)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-59.91,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.04,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-41.53,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.7,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⧵</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3147354" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.653996" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>来<年代vg height="14.6" id="M257" style="vertical-align:-3.13504pt;width:36.862499px;" version="1.1" viewbox="0 0 36.862499 14.6" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，就是这样<年代vg height="10.575" id="M258" style="vertical-align:-0.20064pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.575)">
<g transform="translate(72,-63.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>紧凑。</p><gydF4y2Bah5 id="subsec4.2">4.2。引理的证明<一个href="#lem3.5">3.5</一个></h5>
<p>我们从演示开始<年代vg height="16.237499" id="M259" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，最初定义于<年代vg height="17.674999" id="M260" style="vertical-align:-3.13504pt;width:51.9375px;" version="1.1" viewbox="0 0 51.9375 17.674999" width="51.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.675)">
<g transform="translate(72,-57.86)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,57.91)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-44.72,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.66,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，可简化为算子中<年代vg height="14.6" id="M261" style="vertical-align:-3.13504pt;width:36.862499px;" version="1.1" viewbox="0 0 36.862499 14.6" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。更准确地说，我们证明了这一点<年代vg height="16.237499" id="M262" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>可以实现为某些子空间的订单1的椭圆伪分子运算符<年代vg height="14.6" id="M263" style="vertical-align:-3.13504pt;width:36.862499px;" version="1.1" viewbox="0 0 36.862499 14.6" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有限余维数，因此存在一个常数<年代vg height="11.0625" id="M264" style="vertical-align:-0.30096pt;width:37.8125px;" version="1.1" viewbox="0 0 37.8125 11.0625" width="37.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.852844" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.893232" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>这样<年代p一个nclass="displayed-label" id="eq4.2"><span altimg="C:\WINDOWS\Temp\MMLIMG61695.png" baseline="19" class="displayed" height="47" id="M265" width="452"></span></span>对所有<年代vg height="13.4875" id="M266" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在子空间。</p><p>gydF4y2Ba让<年代vg height="13.4875" id="M267" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="9.9375" id="M268" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于<年代vg height="11.1" id="M269" style="vertical-align:-0.1881pt;width:15.7125px;" version="1.1" viewbox="0 0 15.7125 11.1" width="15.7125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℋ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。同时,让<年代vg height="13.4875" id="M270" style="vertical-align:-2.34499pt;width:49.037498px;" version="1.1" viewbox="0 0 49.037498 13.4875" width="49.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3897533" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.430141" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.682362" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="17.9375" id="M271" style="vertical-align:-2.34499pt;width:50.587502px;" version="1.1" viewbox="0 0 50.587502 17.9375" width="50.587502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.9375)">
<g transform="translate(72,-57.65)">
<text transform="matrix(1,0,0,-1,-71.95,60.03)">
<tspan style="font-size: 12.50px; " x="24.26" y="-2.54">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7898493" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.84" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.09222" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.243694" y="0">
，</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="13.25" id="M272" style="vertical-align:-2.34499pt;width:51.5px;" version="1.1" viewbox="0 0 51.5 13.25" width="51.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.25)">
<g transform="translate(72,-61.4)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.153156" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.193544" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.445766" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们看到(<一个href="#eq4.1">4.1</一个>），<gydF4y2Ba年代p一个nclass="displayed-label" id="eq0028"><span altimg="C:\WINDOWS\Temp\MMLIMG61703.png" baseline="21" class="displayed" height="51" id="M273" width="244"></span></span></p>
<p>更进一步，我们将介绍neumann-to-dirichlet和dirichlet-to-neumann运算符。让<年代vg height="16.6" id="M274" style="vertical-align:-4.74141pt;width:50.974998px;" version="1.1" viewbox="0 0 50.974998 16.6" width="50.974998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.88,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>如在(<一个href="#eq2.2">2.16</一个>）.我们从单层和双层积分算子开始，由<年代p一个nclass="displayed-label" id="eq0029"><span altimg="C:\WINDOWS\Temp\MMLIMG61705.png" baseline="85" class="displayed" height="178" id="M275" width="437"></span></span>最后两个操作符是紧的<年代vg height="14.6" id="M276" style="vertical-align:-3.13504pt;width:36.862499px;" version="1.1" viewbox="0 0 36.862499 14.6" width="36.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-58.22,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，以来，通过lemma<一个href="#lem2.1">2．1</一个>，他们的内核有弱奇点。而且，自核心以来<年代vg height="14.625" id="M277" style="vertical-align:-3.25793pt;width:17.6875px;" version="1.1" viewbox="0 0 17.6875 14.625" width="17.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.625)">
<g transform="translate(72,-60.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和拉普拉斯算子的绿核具有相同的奇异性<年代vg height="13.775" id="M278" style="vertical-align:-0.0pt;width:24.362499px;" version="1.1" viewbox="0 0 24.362499 13.775" width="24.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.775)">
<g transform="translate(72,-60.98)">
<text transform="matrix(1,0,0,-1,-71.95,61.03)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.61,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>(见[<一个href="#B18">18</一个>，第7章，第11节])，我们有以下的极限关系<年代vg height="10.475" id="M279" style="vertical-align:-0.0pt;width:9.3000002px;" version="1.1" viewbox="0 0 9.3000002 10.475" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.475)">
<g transform="translate(72,-63.62)">
<text transform="matrix(1,0,0,-1,-71.95,63.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg><span class="displayed-label" id="eq4.3"><span altimg="C:\WINDOWS\Temp\MMLIMG61710.png" baseline="76" class="displayed" height="160" id="M280" width="167"></span></span>使用绿色类型的公式<年代vg height="10.325" id="M281" style="vertical-align:-0.0pt;width:11.1875px;" version="1.1" viewbox="0 0 11.1875 10.325" width="11.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="10.325" id="M282" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们可以看到,<年代p一个nclass="displayed-label" id="eq0030"><span altimg="C:\WINDOWS\Temp\MMLIMG61713.png" baseline="11" class="displayed" height="31" id="M283" width="157"></span></span>如果我们将其与极限关系相结合（<一个href="#eq4.3">4.5</一个>），我们得到<年代p一个nclass="displayed-label" id="eq0031"><span altimg="C:\WINDOWS\Temp\MMLIMG61714.png" baseline="18" class="displayed" height="44" id="M284" width="238"></span></span></p>
<p>类似的计算<年代vg height="10.6875" id="M285" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>给了<年代p一个nclass="displayed-label" id="eq0032"><span altimg="C:\WINDOWS\Temp\MMLIMG61716.png" baseline="18" class="displayed" height="44" id="M286" width="236"></span></span></p>
<p>做以下定义似乎很自然。<年代p一个nclass="statement" id="deff4.1"><span class="statement-title"><i class="statement-title">定义4.1。</我></年代p一个n>中定义了Dirichlet-to-Neumann算子和Neumann-to-Dirichlet算子<年代vg height="10.325" id="M287" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="10.6875" id="M288" style="vertical-align:-0.0pt;width:11.75px;" version="1.1" viewbox="0 0 11.75 10.6875" width="11.75" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>作为<年代p一个nclass="displayed-label" id="eq0033"><span altimg="C:\WINDOWS\Temp\MMLIMG61719.png" baseline="96" class="displayed" height="200" id="M289" width="209"></span></span></span><span class="statement" id="rem1"><span class="statement-title"><i class="statement-title">4.2的话。</我></年代p一个n>上面的逆至少存在于有限余维空间上。这是由事实得出的<年代vg height="10.55" id="M290" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.55)">
<g transform="translate(72,-63.56)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是椭圆,<年代vg height="10.325" id="M291" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>紧凑。</年代p一个n><年代p一个nclass="statement" id="lem4.2"><span class="statement-title">引理4.3。</年代p一个n><我>操作员<年代vg height="14.6" id="M292" style="vertical-align:-3.13504pt;width:108.4875px;" version="1.1" viewbox="0 0 108.4875 14.6" width="108.4875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.803552" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.680922" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-43.11,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.46,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.340221" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.50372" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="36.021145" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,7.73,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
ω.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个椭圆伪分子经营者的订单<年代vg height="10.6875" id="M293" style="vertical-align:-0.0pt;width:18.65px;" version="1.1" viewbox="0 0 18.65 10.6875" width="18.65" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</我></年代p一个n></p>
<p><span class="statement" id="proof6"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>使用resolvent恒等式，我们可以看到<年代p一个nclass="displayed-label" id="eq0034"><span altimg="C:\WINDOWS\Temp\MMLIMG61724.png" baseline="17" class="displayed" height="49" id="M294" width="320"></span></span>它是由的渐近展开得出的<年代vg height="14.75" id="M295" style="vertical-align:-3.25793pt;width:50.962502px;" version="1.1" viewbox="0 0 50.962502 14.75" width="50.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.9,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.040149" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.241398" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在引理<一个href="#lem2.1">2．1</一个>事实上<年代vg height="14.625" id="M296" style="vertical-align:-3.25793pt;width:17.6875px;" version="1.1" viewbox="0 0 17.6875 14.625" width="17.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.625)">
<g transform="translate(72,-60.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.77,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个Schwartz核(同样，参见[<一个href="#B18">18</一个>（第7章第11节<年代vg height="10.55" id="M297" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.55)">
<g transform="translate(72,-63.56)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个椭圆伪分子经营者的订单<年代vg height="10.6875" id="M298" style="vertical-align:-0.0pt;width:18.65px;" version="1.1" viewbox="0 0 18.65 10.6875" width="18.65" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。此外，运营商<年代vg height="10.325" id="M299" style="vertical-align:-0.0pt;width:11.625px;" version="1.1" viewbox="0 0 11.625 10.325" width="11.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是紧的，那么其他两个因子是阶伪微分算子<年代vg height="10.9125" id="M300" style="vertical-align:-0.17555pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.9125" width="7.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>它不会显著地改变主符号。</年代p一个n></p><p>现在让我们回到表达<年代vg height="10.575" id="M301" style="vertical-align:-0.20064pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.575)">
<g transform="translate(72,-63.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们有<年代p一个nclass="displayed-label" id="eq0035"><span altimg="C:\WINDOWS\Temp\MMLIMG61732.png" baseline="87" class="displayed" height="182" id="M302" width="534"></span></span>既然我们感兴趣<年代vg height="16.237499" id="M303" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>而不是<年代vg height="10.575" id="M304" style="vertical-align:-0.20064pt;width:12.625px;" version="1.1" viewbox="0 0 12.625 10.575" width="12.625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.575)">
<g transform="translate(72,-63.54)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，我们可以假设<年代vg height="13.4875" id="M305" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="9.9375" id="M306" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于<年代vg height="18.9375" id="M307" style="vertical-align:-6.47697pt;width:28.6px;" version="1.1" viewbox="0 0 28.6 18.9375" width="28.6" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.98,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然后<年代vg height="19.862499" id="M308" style="vertical-align:-4.74141pt;width:101.6625px;" version="1.1" viewbox="0 0 101.6625 19.862499" width="101.6625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8625)">
<g transform="translate(72,-56.11)">
<text transform="matrix(1,0,0,-1,-71.95,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.3897533" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.430141" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.682362" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="41.097363" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="53.137749" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-10.03,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,0.84,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="19.862499" id="M309" style="vertical-align:-4.74141pt;width:103.1375px;" version="1.1" viewbox="0 0 103.1375 19.862499" width="103.1375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.8625)">
<g transform="translate(72,-56.11)">
<text transform="matrix(1,0,0,-1,-71.95,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.153156" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.193544" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.445766" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.073074" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="56.113464" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-7.06,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="8.2700005">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,3.81,60.89)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。对于这样的<年代vg height="13.4875" id="M310" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="9.9375" id="M311" style="vertical-align:-2.34499pt;width:8.4375px;" version="1.1" viewbox="0 0 8.4375 9.9375" width="8.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.9375)">
<g transform="translate(72,-64.05)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们得到了<年代p一个nclass="displayed-label" id="eq0036"><span altimg="C:\WINDOWS\Temp\MMLIMG61742.png" baseline="21" class="displayed" height="56" id="M312" width="410"></span></span>或者使用上面介绍的运算符<年代p一个nclass="displayed-label" id="eq4.4"><span altimg="C:\WINDOWS\Temp\MMLIMG61743.png" baseline="25" class="displayed" height="65" id="M313" width="503"></span></span>而且，<年代vg height="14.6" id="M314" style="vertical-align:-3.13504pt;width:46.012501px;" version="1.1" viewbox="0 0 46.012501 14.6" width="46.012501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.040869" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.680922" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-43.11,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个椭圆伪分子经营者的订单<年代vg height="10.6875" id="M315" style="vertical-align:-0.0pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.6875" width="7.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。这是从身份出发的<年代vg height="14.6" id="M316" style="vertical-align:-3.13504pt;width:144.425px;" version="1.1" viewbox="0 0 144.425 14.6" width="144.425" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9646511" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.12815" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.00552" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.645573" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.14,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.8,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.50564" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.858364" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.021862" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.273361" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="48.749195" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.000698" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="59.164196" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，事实是<年代vg height="10.55" id="M317" style="vertical-align:-0.0pt;width:11.325px;" version="1.1" viewbox="0 0 11.325 10.55" width="11.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.55)">
<g transform="translate(72,-63.56)">
<text transform="matrix(1,0,0,-1,-71.95,63.61)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个椭圆伪分子经营者的订单<年代vg height="10.6875" id="M318" style="vertical-align:-0.0pt;width:18.65px;" version="1.1" viewbox="0 0 18.65 10.6875" width="18.65" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。它来自(<一个href="#eq4.4">4.13</一个>），<gydF4y2Ba年代vg height="16.237499" id="M319" style="vertical-align:-4.74141pt;width:16px;" version="1.1" viewbox="0 0 16 16.237499" width="16" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是椭圆伪微分算子还是阶<年代vg height="10.6875" id="M320" style="vertical-align:-0.0pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.6875" width="7.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba接下来我们证明不等式(<一个href="#eq3.3">3.10</一个>）.由于投影，它足以向功能展示<年代vg height="13.4875" id="M321" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在<年代vg height="18.9375" id="M322" style="vertical-align:-6.47697pt;width:32.5px;" version="1.1" viewbox="0 0 32.5 18.9375" width="32.5" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-60.12,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.98,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-49.17,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
。</gydF4y2Batspan>
</text>
</g>
</g>
</svg></p>
<p><i>的下界</我>。我们证明了子空间的存在<年代vg height="23.512501" id="M323" style="vertical-align:-6.47697pt;width:59.599998px;" version="1.1" viewbox="0 0 59.599998 23.512501" width="59.599998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,23.5125)">
<g transform="translate(72,-53.19)">
<text transform="matrix(1,0,0,-1,-70.81,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-1.14" y="2.8699999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.61306" y="2.8699999">
⊂</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.653448" y="2.8699999">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.32,56.57)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.18,54.38)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有限余维的，使(<一个href="#eq3.3">3.10</一个>）对所有人有效<年代vg height="18.362499" id="M324" style="vertical-align:-2.34499pt;width:39.799999px;" version="1.1" viewbox="0 0 39.799999 18.362499" width="39.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.3625)">
<g transform="translate(72,-57.31)">
<text transform="matrix(1,0,0,-1,-71.95,59.7)">
<tspan style="font-size: 12.50px; " x="23.59" y="-2.8699999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.450001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
∈</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。自<年代vg height="18.9375" id="M325" style="vertical-align:-6.47697pt;width:56.662498px;" version="1.1" viewbox="0 0 56.662498 18.9375" width="56.662498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.9375)">
<g transform="translate(72,-56.85)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.67,60.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.53,58.05)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>我们有<年代vg height="16.6" id="M326" style="vertical-align:-4.74141pt;width:147.78751px;" version="1.1" viewbox="0 0 147.78751 16.6" width="147.78751" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.27,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
∶</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.791529" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="28.831919" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.995419" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.623207" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="55.975929" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,7.48,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,13.31,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.565995" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.606384" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>所以<年代vg height="13.4875" id="M327" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>属于二阶椭圆算子的核<年代vg height="16.237499" id="M328" style="vertical-align:-4.74141pt;width:18.475px;" version="1.1" viewbox="0 0 18.475 16.237499" width="18.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。让<年代vg height="14.6" id="M329" style="vertical-align:-3.13504pt;width:48.762501px;" version="1.1" viewbox="0 0 48.762501 14.6" width="48.762501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6)">
<g transform="translate(72,-60.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.790329" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.830717" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.769882" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.67,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
γ.</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们研究这个问题<年代p一个nclass="displayed-label" id="eq4.5"><span altimg="C:\WINDOWS\Temp\MMLIMG61760.png" baseline="28" class="displayed" height="64" id="M330" width="143"></span></span>让<年代vg height="13.55" id="M331" style="vertical-align:-2.29482pt;width:44.549999px;" version="1.1" viewbox="0 0 44.549999 13.55" width="44.549999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.55)">
<g transform="translate(72,-61.16)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9271421" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.090641" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.967291" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.168539" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.370028" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是的Schwartz核<年代vg height="16.237499" id="M332" style="vertical-align:-4.74141pt;width:18.475px;" version="1.1" viewbox="0 0 18.475 16.237499" width="18.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。从对角线往外是光滑的<年代vg height="9.875" id="M333" style="vertical-align:-2.29482pt;width:35.862499px;" version="1.1" viewbox="0 0 35.862499 9.875" width="35.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。我们可以用单层和双层的势来重复这个理论<年代vg height="16.237499" id="M334" style="vertical-align:-4.74141pt;width:18.475px;" version="1.1" viewbox="0 0 18.475 16.237499" width="18.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>写出解<年代vg height="13.4875" id="M335" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在这种情况下它是存在的。</p><p>gydF4y2Ba让<年代vg height="16.237499" id="M336" style="vertical-align:-4.74141pt;width:18.2875px;" version="1.1" viewbox="0 0 18.2875 16.237499" width="18.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.25,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>为双层算子在边界处求值，<年代p一个nclass="displayed-label" id="eq0037"><span altimg="C:\WINDOWS\Temp\MMLIMG61767.png" baseline="10" class="displayed" height="38" id="M337" width="344"></span></span>操作员<年代vg height="16.237499" id="M338" style="vertical-align:-4.74141pt;width:18.2875px;" version="1.1" viewbox="0 0 18.2875 16.237499" width="18.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.25,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是紧凑型的，自从内核<年代vg height="16.6" id="M339" style="vertical-align:-4.74141pt;width:67.900002px;" version="1.1" viewbox="0 0 67.900002 16.6" width="67.900002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-65.56,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="7.4479518" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.27,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="8.9271421" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.090641" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.967291" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.168539" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.370028" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在对角线上有弱奇点吗<年代vg height="9.875" id="M340" style="vertical-align:-2.29482pt;width:35.862499px;" version="1.1" viewbox="0 0 35.862499 9.875" width="35.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.875)">
<g transform="translate(72,-64.1)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.339981" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.380369" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。因此存在一个子空间<年代vg height="14.6625" id="M341" style="vertical-align:-3.13504pt;width:73.962502px;" version="1.1" viewbox="0 0 73.962502 14.6625" width="73.962502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6625)">
<g transform="translate(72,-60.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.66,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-54.31,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⊂</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-33.42,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-28.55,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.50276" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有限余维数，使算子<年代vg height="16.6" id="M342" style="vertical-align:-4.74141pt;width:73.824997px;" version="1.1" viewbox="0 0 73.824997 16.6" width="73.824997" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.890833" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.142332" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.305832" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.082939" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.423161" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-18.82,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是可逆的<年代vg height="14.6625" id="M343" style="vertical-align:-3.13504pt;width:17.825001px;" version="1.1" viewbox="0 0 17.825001 14.6625" width="17.825001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6625)">
<g transform="translate(72,-60.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-62.66,60.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。因此，存在一个子空间<年代vg height="23.512501" id="M344" style="vertical-align:-6.47697pt;width:59.599998px;" version="1.1" viewbox="0 0 59.599998 23.512501" width="59.599998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,23.5125)">
<g transform="translate(72,-53.19)">
<text transform="matrix(1,0,0,-1,-70.81,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-1.14" y="2.8699999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.61306" y="2.8699999">
⊂</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="23.653448" y="2.8699999">
ℒ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-35.32,56.57)">
<tspan style="font-size: 8.75px; " x="0" y="0">
λ.</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-29.18,54.38)">
<tspan style="font-size: 6.25px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>有限的Codimension，我们有代表公式<年代p一个nclass="displayed-label" id="eq4.6"><span altimg="C:\WINDOWS\Temp\MMLIMG61775.png" baseline="25" class="displayed" height="53" id="M345" width="430"></span></span>对所有<年代vg height="18.362499" id="M346" style="vertical-align:-2.34499pt;width:39.799999px;" version="1.1" viewbox="0 0 39.799999 18.362499" width="39.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,18.3625)">
<g transform="translate(72,-57.31)">
<text transform="matrix(1,0,0,-1,-71.95,59.7)">
<tspan style="font-size: 12.50px; " x="23.59" y="-2.8699999">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.450001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
∈</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。不平等<年代vg height="17.6625" id="M347" style="vertical-align:-5.41734pt;width:143.45px;" version="1.1" viewbox="0 0 143.45 17.6625" width="143.45" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.6625)">
<g transform="translate(72,-57.87)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
‖</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.966091" y="0">
‖</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-50.43,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-44.24,58.01)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.61,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-31.03,58.01)">
<tspan style="font-size: 6.25px; " x="0" y="0">
0</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-27.4,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-20.52,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.417398" y="0">
‖</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.956469" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.395992" y="0">
‖</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,21.43,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,27.62,58.01)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,31.25,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.0518398" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>很容易从(<一个href="#eq4.6">4.16</一个>）<gydF4y2Ba年代vg height="13.4875" id="M348" style="vertical-align:-2.34499pt;width:10.675px;" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。</p><p>gydF4y2Ba因为我们也有<年代vg height="17.549999" id="M349" style="vertical-align:-5.32956pt;width:139.8px;" version="1.1" viewbox="0 0 139.8 17.549999" width="139.8" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.55)">
<g transform="translate(72,-57.96)">
<text transform="matrix(1,0,0,-1,-71.95,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
‖</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.5390692" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="14.966091" y="0">
‖</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-50.43,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-44.24,58.01)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.61,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.0518398" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-25.67,63.32)">
<tspan style="font-size: 12.50px; " x="0" y="0">
≤</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.417398" y="0">
‖</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.956469" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="35.395992" y="0">
‖</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,16.27,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,24.7,63.57)">
<tspan style="font-size: 6.25px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,28.32,60.2)">
<tspan style="font-size: 8.75px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="2.9144161" y="0">
γ.</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.0518398" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的下界(<一个href="#eq3.3">3.10</一个>）通过下限（<一个href="#eq4.2">4.2</一个>）.</p><p><我>的上限</我>。通过上限（<一个href="#eq4.2">4.2</一个>），这足以说明下列不平等<年代p一个nclass="displayed-label" id="eq0038"><span altimg="C:\WINDOWS\Temp\MMLIMG61780.png" baseline="18" class="displayed" height="39" id="M350" width="594"></span></span>然而，第一个不平等只是痕迹定理，第二个是嵌入定理的SoboLev-Rellich。我们注意到,<年代vg height="16.6" id="M351" style="vertical-align:-4.74141pt;width:54.349998px;" version="1.1" viewbox="0 0 54.349998 16.6" width="54.349998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.1,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-57.27,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.402496" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>第三个不等式是椭圆算子的标准估计。</p><gydF4y2Bah4 id="spectrum-of-toeplitz-operators-in-a-reinhardt-domain">5.Reinhardt域上Toeplitz算子的谱</gydF4y2Bah4>
<p>在这种情况下<年代vg height="10.325" id="M352" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>莱因哈特领域是一个可以加强的部分吗<年代vg height="13.45" id="M353" style="vertical-align:-2.21957pt;width:17.875px;" version="1.1" viewbox="0 0 17.875 13.45" width="17.875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.45)">
<g transform="translate(72,-61.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.039909" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>lemma.<一个href="#lem3.6">3.6</一个>。假设<年代vg height="10.6125" id="M354" style="vertical-align:-0.0pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 10.6125" width="17.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.42,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的内部<年代vg height="10.325" id="M355" style="vertical-align:-0.0pt;width:13.2875px;" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，是雷皮特域。这意味着<年代vg height="11.1125" id="M356" style="vertical-align:-0.33858pt;width:44.9375px;" version="1.1" viewbox="0 0 44.9375 11.1125" width="44.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1125)">
<g transform="translate(72,-63.11)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7148314" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.75522" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.66,68.5)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>而如果<年代vg height="11.0375" id="M357" style="vertical-align:-0.33858pt;width:44.924999px;" version="1.1" viewbox="0 0 44.924999 11.0375" width="44.924999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0375)">
<g transform="translate(72,-63.17)">
<text transform="matrix(1,0,0,-1,-71.95,63.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7023277" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.742718" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.67,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，则集合<年代p一个nclass="displayed-label" id="eq0039"><span altimg="C:\WINDOWS\Temp\MMLIMG61788.png" baseline="15" class="displayed" height="39" id="M358" width="323"></span></span>是<年代vg height="10.6125" id="M359" style="vertical-align:-0.0pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 10.6125" width="17.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.42,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。如果一组<年代p一个nclass="displayed-label" id="eq0040"><span altimg="C:\WINDOWS\Temp\MMLIMG61790.png" baseline="15" class="displayed" height="39" id="M360" width="370"></span></span>是通常意义上的凸吗<年代vg height="10.6125" id="M361" style="vertical-align:-0.0pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 10.6125" width="17.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.42,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是对数凸的，那么<年代vg height="10.6125" id="M362" style="vertical-align:-0.0pt;width:17.737499px;" version="1.1" viewbox="0 0 17.737499 10.6125" width="17.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6125)">
<g transform="translate(72,-63.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.56)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-61.42,68.56)">
<tspan style="font-size: 8.75px; " x="0" y="0">
∘</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是一个全纯域。表示由<年代vg height="17.5875" id="M363" style="vertical-align:-3.13504pt;width:94.425003px;" version="1.1" viewbox="0 0 94.425003 17.5875" width="94.425003" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,17.5875)">
<g transform="translate(72,-57.93)">
<text transform="matrix(1,0,0,-1,-71.95,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-64.76,57.98)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-53.42,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
∶</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.8523636" y="0">
ℝ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-34.22,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-22.98,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
→</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.12911" y="0">
ℝ</gydF4y2Batspan>
</text>
</g>
</g>
</svg>由<年代p一个nclass="displayed-label" id="eq0041"><span altimg="C:\WINDOWS\Temp\MMLIMG61794.png" baseline="23" class="displayed" height="55" id="M364" width="193"></span></span>我们表示<年代vg height="20.862499" id="M365" style="vertical-align:-3.80708pt;width:257.375px;" version="1.1" viewbox="0 0 257.375 20.862499" width="257.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.8625)">
<g transform="translate(72,-55.31)">
<text transform="matrix(1,0,0,-1,-71.95,59.15)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.214951" y="0">
∶</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.079819" y="0">
ℱ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.37,64.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.0200005">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-27.88,59.15)">
<tspan style="font-size: 12.50px; " x="0" y="0">
→</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.26" y="-2.96">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.139999" y="0">
ℋ</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.068821" y="0">
∶</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.457855" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="51.498245" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,32.48,56.02)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,37.35,59.15)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="13.690785" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.892033" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,61.81,64.15)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="8.9095364" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="15.000928" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="17.433985" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="23.271568" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="26.185984" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="27.936384" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="32.303631" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,95.87,67.72)">
<tspan style="font-size: 6.25px; " x="0" y="0">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,99.99,59.15)">
<tspan style="font-size: 12.50px; " x="0" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.12863" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.29213" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.531126" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="29.694626" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>嵌入操作符。的<年代vg height="7.1875" id="M366" style="vertical-align:-0.13794pt;width:7px;" version="1.1" viewbox="0 0 7 7.1875" width="7" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.1875)">
<g transform="translate(72,-66.25)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>值<年代vg height="13.375" id="M367" style="vertical-align:-5.27927pt;width:16.9125px;" version="1.1" viewbox="0 0 16.9125 13.375" width="16.9125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.375)">
<g transform="translate(72,-61.3)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.71" y="5.0900002">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.5099521" y="5.0900002">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，<年代vg height="14.1" id="M368" style="vertical-align:-0.33858pt;width:46.799999px;" version="1.1" viewbox="0 0 46.799999 14.1" width="46.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.1)">
<g transform="translate(72,-60.72)">
<text transform="matrix(1,0,0,-1,-71.74,61.1)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.677562" y="0">
∈</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
ℕ</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-40.29,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>的,<年代vg height="10.5125" id="M369" style="vertical-align:-0.15048pt;width:10.4375px;" version="1.1" viewbox="0 0 10.4375 10.5125" width="10.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.5125)">
<g transform="translate(72,-63.59)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>与数字一致<年代p一个nclass="displayed-label" id="eq5.1"><span altimg="C:\WINDOWS\Temp\MMLIMG61800.png" baseline="37" class="displayed" height="76" id="M370" width="124"></span></span>(我们提醒读者在引理中特征值的符号<一个href="#lem3.6">3.6</一个>）.与案例<年代vg height="10.875" id="M371" style="vertical-align:-0.15048pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 10.875" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>,<一个href="#B4">10</一个>］以自然为特征值是自然的<年代vg height="10.75" id="M372" style="vertical-align:-0.15048pt;width:9.375px;" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.75)">
<g transform="translate(72,-63.4)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>元组<年代vg height="16.15" id="M373" style="vertical-align:-3.24037pt;width:102.225px;" version="1.1" viewbox="0 0 102.225 16.15" width="102.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.15)">
<g transform="translate(72,-59.08)">
<text transform="matrix(1,0,0,-1,-71.74,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="-0.200048" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.677562" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.717951" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.881451" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-37.42,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-32.55,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
．..</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.79225" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="25.006001" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-0.11,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,5.56,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，就像单位立方体中拉普拉斯算子的特征值一样<年代vg height="16.3375" id="M374" style="vertical-align:-1.95624pt;width:39.775002px;" version="1.1" viewbox="0 0 39.775002 16.3375" width="39.775002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.3375)">
<g transform="translate(72,-58.93)">
<text transform="matrix(1,0,0,-1,-71.95,60.93)">
<tspan style="font-size: 12.50px; " x="0" y="0">
［</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
0</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.616247" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.867746" y="0">
］</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-45.91,66.1)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>，特征值给出的地方<年代vg height="19.299999" id="M375" style="vertical-align:-4.26343pt;width:220.325px;" version="1.1" viewbox="0 0 220.325 19.299999" width="220.325" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,19.3)">
<g transform="translate(72,-56.56)">
<text transform="matrix(1,0,0,-1,-71.95,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.00432" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-49.77,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-38.1,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.713151" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="2.513103" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.9273825" y="0">
|</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-25.67,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.21">
2</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-17.32,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="16.191385" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.442884" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.044708" y="0">
）</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,16.9,66.03)">
<tspan style="font-size: 8.75px; " x="0" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="5.99512" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,28.57,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,40.16,65.87)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.2200003">
1</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,47.82,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.327718" y="0">
⋯</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="27.769163" y="0">
+</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="39.121887" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,94.37,65.87)">
<tspan style="font-size: 8.75px; " x="0" y="0">
2</gydF4y2Batspan>
<tspan style="font-size: 8.75px; " x="0" y="9.1499996">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,100.05,60.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。<年代p一个nclass="statement" id="lem5.1"><span class="statement-title">引理5.1。</年代p一个n><我>让<年代vg height="11.0625" id="M376" style="vertical-align:-0.30096pt;width:35.637501px;" version="1.1" viewbox="0 0 35.637501 11.0625" width="35.637501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="10.114927" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="22.155315" y="0">
1</gydF4y2Batspan>
</text>
</g>
</g>
</svg>和<年代vg height="14.875" id="M377" style="vertical-align:-2.21957pt;width:59.325001px;" version="1.1" viewbox="0 0 59.325001 14.875" width="59.325001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.875)">
<g transform="translate(72,-60.1)">
<text transform="matrix(1,0,0,-1,-71.95,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.977874" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.230814" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.030766" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="31.445045" y="0">
/</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="34.920879" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.634029" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="37.433983" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="44.848263" y="0">
|</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。然后</我><年代p一个nclass="displayed-label" id="eq5.2"><span altimg="C:\WINDOWS\Temp\MMLIMG61808.png" baseline="19" class="displayed" height="47" id="M378" width="417"></span></span><i></i></span></p>
<p><span class="statement" id="proof7"><span class="statement-title"><i class="statement-title">证明。</我></年代p一个n>分母在（<一个href="#eq5.1">5．4</一个>）很容易计算出来<年代p一个nclass="displayed-label" id="eq0042"><span altimg="C:\WINDOWS\Temp\MMLIMG61809.png" baseline="17" class="displayed" height="50" id="M379" width="203"></span></span>对于分子，我们从上到下进行估计，如[<一个href="#B9">12</一个>］．首先,请注意,<年代p一个nclass="displayed-label" id="eq0043"><span altimg="C:\WINDOWS\Temp\MMLIMG61810.png" baseline="21" class="displayed" height="51" id="M380" width="332"></span></span>在哪里<年代vg height="14.6125" id="M381" style="vertical-align:-2.21957pt;width:38.037498px;" version="1.1" viewbox="0 0 38.037498 14.6125" width="38.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.6125)">
<g transform="translate(72,-60.31)">
<text transform="matrix(1,0,0,-1,-71.95,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.7268538" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.12863" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.29213" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.168779" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是变换后的测度。很明显<年代p一个nclass="displayed-label" id="eq0044"><span altimg="C:\WINDOWS\Temp\MMLIMG61812.png" baseline="9" class="displayed" height="27" id="M382" width="235"></span></span>对于另一个方向的不等式，固定<年代vg height="11.0625" id="M383" style="vertical-align:-0.30096pt;width:35.1875px;" version="1.1" viewbox="0 0 35.1875 11.0625" width="35.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0625)">
<g transform="translate(72,-63.15)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.7523403" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="21.792728" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。超平面<年代p一个nclass="displayed-label" id="eq0045"><span altimg="C:\WINDOWS\Temp\MMLIMG61814.png" baseline="9" class="displayed" height="27" id="M384" width="163"></span></span>削减<年代vg height="14.2" id="M385" style="vertical-align:-2.73372pt;width:40.862499px;" version="1.1" viewbox="0 0 40.862499 14.2" width="40.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2)">
<g transform="translate(72,-60.64)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">
l</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="3.4758339" y="0">
o</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">
g</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="18.054333" y="0">
|</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="20.554932" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="30.082218" y="0">
|</gydF4y2Batspan>
</text>
</g>
</g>
</svg>在两个组件。让<年代vg height="14.3625" id="M386" style="vertical-align:-3.2316pt;width:15.5375px;" version="1.1" viewbox="0 0 15.5375 14.3625" width="15.5375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3625)">
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<text transform="matrix(1,0,0,-1,-71.95,63.79)">
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<text transform="matrix(1,0,0,-1,-64.52,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
</g>
</g>
</svg>是不等式的分量<年代vg height="16.025" id="M387" style="vertical-align:-3.13504pt;width:138.66251px;" version="1.1" viewbox="0 0 138.66251 16.025" width="138.66251" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.025)">
<g transform="translate(72,-59.18)">
<text transform="matrix(1,0,0,-1,-71.95,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
⟨</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="5.2012482" y="0">
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<tspan style="font-size: 12.50px; " x="5.0012002" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.415479" y="0">
，</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="17.62923" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="24.50588" y="0">
⟩</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="32.982914" y="0">
≥</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.023304" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="49.186802" y="0">
1</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="58.213966" y="0">
−</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="69.554192" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="75.843201" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="80.006699" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,15.25,59.23)">
<tspan style="font-size: 8.75px; " x="0" y="0">
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</text>
<text transform="matrix(1,0,0,-1,23.12,62.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.37605" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="4.176002" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">
）</gydF4y2Batspan>
</text>
</g>
</g>
</svg>成立。然后我们有<年代p一个nclass="displayed-label" id="eq0046"><span altimg="C:\WINDOWS\Temp\MMLIMG61818.png" baseline="21" class="displayed" height="51" id="M388" width="551"></span></span>在哪里<年代vg height="21.375" id="M389" style="vertical-align:-6.74023pt;width:119.8375px;" version="1.1" viewbox="0 0 119.8375 21.375" width="119.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,21.375)">
<g transform="translate(72,-54.9)">
<text transform="matrix(1,0,0,-1,-71.95,61.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-63.56,58.55)">
<tspan style="font-size: 8.75px; " x="0" y="0">
</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-55.19,61.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
＝</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="12.04" y="0.02">
∫</gydF4y2Batspan>
</text>
<text transform="matrix(1,0,0,-1,-39.7,57.21)">
<tspan style="font-size: 8.75px; " x="0" y="0">
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</text>
<text transform="matrix(1,0,0,-1,-34.5,55.02)">
<tspan style="font-size: 6.25px; " x="0" y="0">
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</text>
<text transform="matrix(1,0,0,-1,-28.28,61.67)">
<tspan style="font-size: 12.50px; " x="0" y="0">
d</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="7.739357" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="6.2640028" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="15.141133" y="0">
（</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="19.304632" y="0">
</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="26.181282" y="0">
）</gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="33.808113" y="0">
></gydF4y2Batspan>
<tspan style="font-size: 12.50px; " x="45.835999" y="0">
0</gydF4y2Batspan>
</text>
</g>
</g>
</svg>。由此可见,<年代p一个nclass="displayed-label" id="eq0047"><span altimg="C:\WINDOWS\Temp\MMLIMG61820.png" baseline="72" class="displayed" height="152" id="M390" width="422"></span></span>的(<一个href="#eq5.2">5．5</一个>）。</年代p一个n></p><h4 id="acknowledgment">承认</gydF4y2Bah4>
<p>作者要感谢他的导师，Grigori Rozenblum教授，是他向他介绍了这个问题，并给予了他所需要的一切支持。</p></d我v>
<div class="xml-content">
<h4 class="references" id="references">参考</gydF4y2Bah4>
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</ol>
</div>
<div class="xml-content">
<h4 class="copyright" id="copyright">版权</gydF4y2Bah4>
<p>Mikael Persson版权所有。这是一篇开放获取的文章<一个rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享署名许可</一个>，允许在任何媒介上不受限制地使用、分发和复制，只要原稿被适当引用。</p></d我v>
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<a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-cBdUnI bmjKRX pdf_desktop button__group" href="https://downloads.hindawi.com/journals/amp/2009/873704.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="https://static-01.hindawi.com/next_assets/lDWlMLx7CjNkKVv6zTYqv/_next/static/node_modules/hindawi-ui/src/icon/svg/pdf.svg" height="24"><span class="text">PDF</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a>
<a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo huSjso ref_desktop" href="//www.newsama.com/journals/amp/2009/873704.ris" aria-label="" target="" id="toolbar__dcNavLarge"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a>
<a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-kcDeIU cpLlMu ref_desktop" href="//www.newsama.com/journals/amp/2009/873704.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">引用</年代p一个n></年代p一个n><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a>
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<span><img alt="" class="sc-EHOje jOLhQl sc-eAKXzc bESoPs" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-gbOuXE SDMqt">下载其他格式</年代p一个n><年代p一个nclass="sc-dRFtgE jooXYL">更多的</年代p一个n></年代p一个n>
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XML.</d我v><img alt="" class="sc-EHOje jOLhQl sc-eAKXzc bESoPs" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"></a>
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<div class="sc-cqpYsc krPIEq">
<div class="sc-hBbWxd hdkxPJ">
<div>
的观点<年代p一个n>790</gydF4y2Ba年代p一个n></d我v>
<div>
下载<年代p一个n>527</gydF4y2Ba年代p一个n></d我v>
</div>
<div>
<div class="sc-dyGzUR cmbuIE">
<span class="__dimensions_badge_embed__" data-doi="10.1155/2009/873704" data-style="small_circle"></span>引用</d我v>
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<h3 class="sc-Rmtcm hNPrIr">分享文章</gydF4y2Bah3>
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