Uniform continuity and quantization on bounded symmetric domains

Bauer Wolfram; Hagger Raffael; Vasilevski Nikolai

摘要

Abstract > We consider Toeplitz operators <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12069:jlms12069-math-0001" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12069-math-0001.png"> <mat:msubsup> <mat:mi>T</mat:mi> <mat:mi>f</mat:mi> <mat:mi>λ</mat:mi> </mat:msubsup> </mat:math> with symbol <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12069:jlms12069-math-0002" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12069-math-0002.png"> <mat:mi>f</mat:mi> </mat:math> acting on the standard weighted Bergman spaces over a bounded symmetric domain <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12069:jlms12069-math-0003" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12069-math-0003.png"> <mat:mrow> <mat:mi mathvariant="normal">Ω</mat:mi> <mat:mo>?</mat:mo> <mat:msup> <mat:mi mathvariant="double-struck">C</mat:mi> <mat:mi>n</mat:mi> </mat:msup> </mat:mrow> </mat:math> . Here <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12069:jlms12069-math-0004" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12069-math-0004.png"> <mat:mrow> <mat:mi>λ</mat:mi> <mat:mo></mat:mo> <mat:mtext mathvariant="italic">genus</mat:mtext> <mat:mo>?</mat:mo> <mat:mn>1</mat:mn> </mat:mrow> </mat:math> is the weight parameter. The classical asymptotic relation for the semi‐commutator <displayedItem xml:id="jlms12069-disp-0001" type="mathematics"> <label>*</label> <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="block" altimg="urn:x-wiley:00246107:media:jlms12069:jlms12069-math-0005" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12069-math-0005.png"> <mat:mrow> <mat:munder> <mat:mo movablelimits="true" form="prefix">lim</mat:mo> <mat:mrow> <mat:mi>λ</mat:mi> <mat:mo>→</mat:mo> <mat:mi>∞</mat:mi> </mat:mrow> </mat:munder> <mat:msub> <mat:mfenced separators="" open="‖" close="‖"> <mat:msubsup> <mat:mi>T</mat:mi> <mat:mi>f</mat:mi> <mat:mi>λ</mat:mi> </mat:msubsup> <mat:msubsup> <mat:mi>T</mat:mi> <mat:mi>g</mat:mi> <mat:mi>λ</mat:mi> </mat:msubsup> <mat:mo>?</mat:mo> <mat:msubsup> <mat:mi>T</mat:mi> <mat:mrow> <mat:mi>f</mat:mi> <mat:mi>g</mat:mi> </mat:mrow> <mat:mi>λ</mat:mi> </mat:msubsup> </mat:mfenced> <mat:mi>λ</mat:mi> </mat:msub> <mat:mo>=</mat:mo> <mat:mn>0</mat:mn> <mat:mo>,</mat:mo> <mat:mspace width="1em"/> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract XMLNS =“http://www.wiley.com/namespaces/wiley”type =“main”> <title type =“main”>抽象</ title> >我们认为toeplitz运算符<mat：math xmlns ：mat =“http://www.w3.org/1998/math/mathml”display =“内联”altimg =“urn：x-wiley：00246107：媒体：jlms12069：jlms12069-math-0001”XMLNS：Wiley = “http://www.wiley.com/namespaces/wiley/wiley”wiley：location =“等式/ jlms12069-math-0001.png”> <mat：msubsup> <mat：mi> t </ mat：mi> <mat：m> f </ mat：mi> <mat：mi>λ</ mat：mi> </ mat：msubsup> </ mat：math>与符号<mat：math xmlns：mat =“http：/ / www.w3.org/1998/math/mathml“display =”内联“altimg =”urn：x-wiley：00246107：媒体：jlms12069：jlms12069-math-0002“xmlns：wiley =”http：// www。 wiley.com/namespaces/wiley/wiley“wiley：location =”等式/ jlms12069-math-0002.png“> <mat：mi> f </ mat：mi> </ mat：math>在标准加权伯格曼行事界限对称域中的空间<mat：math xmlns：mat =“http://www.w3.org/1998/math/mathml”display =“内联”altimg =“urn：x-wiley：00246107：媒体：jlms12069 ：JLMS12069-MATH-0003“XM lns：wiley =“http://www.wiley.com/namespaces/wiley/wiley”wiley：location =“等式/ jlms12069-math-0003.png”> <mat：mrow> <mat：mi mathvariant =“正常“>ω</ mat：mi> <mat：mo>？</ mat：mo> <mat：msup> <mat：mi mathvariant =”双击“> c </ mat：mi> <mat：mi> n </ mat：mi> </ mat：msup> </ mat：mrow> </ mat：math>。这里<mat：math xmlns：mat =“http://www.w3.org/1998/math/mathml”display =“内联”altimg =“urn：x-wiley：00246107：媒体：jlms12069：jlms12069-数学 - 0004“XMLNS：Wiley =”http://www.wiley.com/namespaces/wiley/wiley“wiley：location =”等式/ jlms12069-math-0004.png“> <mat：mrow> <mat：mi>λ </ mat：<mat：mo>＆ </ mat：mo> <mat：mtext mathvariant =“italic”> genus </ mat：mtext> <mat：mo>？</ mat：mo> <mo ：Mn> 1 </ mat：Mn> </ mat：MROW> </ MAT：MATH>是权重参数。半换向器的经典渐近关系<lightsitem xml：id =“jlms12069-disp-0001”类型=“数学”> <label> * </ label> <mat：math xmlns：mat =“http：// www .w3.org / 1998 / math / mathml“display =”块“Altimg =”URN：X-Wiley：00246107：媒体：JLMS12069：JLMS12069-Math-0005“XMLNS：Wiley =”http：//www.wiley。 com / namespaces / wiley / wiley“wiley：location =”等式/ jlms12069-math-0005.png“> <mat：mrow> <mat：munder> <mat：mo movablelimits =”true“形式=”prefix“> lim </ mat：<may：mrow> <mat：mi>λ</ mat：mi> <mat：mo>→</ mat：mo> <mat：mi>∞</ mat：mi> </ mat ：MROW> </ MAT：MURSE> <MAT：MSUB> <MAT：MFENCED SETCHITALER =“”OPEN =“‖”关闭=“‖”> <MAT：MSUBSUP> <MAT：MI> T </ MAT：MI> <MAT：F </ MAT：MI> <MAT：MI>λ</ MAT：MI> </ MAT：MSUBSUP> <MAT：MSUBSUP> <MAT：MI> T </ MAT：MI> <MAT： mi> g </ mat：mi> <mat：mi>λ</ mat：mi> </ mat：msubsup> <mat：mo>？</ mat：mo> <mat：msubsup> <mat：mi> t </ MAT：MI> <MAT：MROW> <MAT：MI> F </ MAT：MI> <MAT：MI> G </ MAT：MI> </ MAT：MROW> <MAT：MI>λ</垫：mi> </ mat：msubsup> </ mat：mfeced> <mat：mi>λ</ mat：mi> </ mat：msub> <mat：mo> = </ mat：m o> <mat：0 </ mat：mn> <mat：mo>，</ mo：mo> <mat：mspace width =“1em”/> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-31023/'>《The Journal of the London Mathematical Society》</a> <b style="margin: 0 2px;">|</b><span>2017年第2期</span><b style="margin: 0 2px;">|</b><span>共22页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bauer Wolfram&option=202" target="_blank" rel="nofollow">Bauer Wolfram;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hagger Raffael&option=202" target="_blank" rel="nofollow">Hagger Raffael;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Vasilevski Nikolai&option=202" target="_blank" rel="nofollow">Vasilevski Nikolai;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Fakult?t für Mathematik und PhysikInstitut für AnalysisWelfengarten 1 30167 Hannover Germany;</p> <p>Fakult?t für Mathematik und PhysikInstitut für AnalysisWelfengarten 1 30167 Hannover Germany;</p> <p>Departamento de MatemáticasCINVESTAVApartado Postal 14‐740 07000 México D.F. México;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=47B35 (primary)&option=203" rel="nofollow">47B35 (primary);</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=81S10&option=203" rel="nofollow">81S10;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=32M15 (secondary)&option=203" rel="nofollow">32M15 (secondary);</a> </p> <div class="translation"> 机译：47B35（初级）;81S10;32M15（二次）; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024866731.html">Uniform continuity and quantization on bounded symmetric domains</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Bauer Wolfram&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Bauer Wolfram,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hagger Raffael&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Hagger Raffael,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Vasilevski Nikolai&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Vasilevski Nikolai </a> <a href="/journal-foreign-31023/" target="_blank" rel="nofollow" class="tuijian_authcolor">The Journal of the London Mathematical Society .</a> <span>2017</span><span>,第2期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：界限对称域的均匀连续性和量化</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070406513249.html">Toeplitz quantization and asymptotic expansions for real bounded symmetric domains</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Engli? 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