The Zak transform on strongly proper <mat:math xmlns:mat='http://www.w3.org/1998/Math/MathML' display='inline' altimg='urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0001' xmlns:wiley='http://www.wiley.com/namespaces/wiley/wiley' wiley:location='equation/jlms12097-math-0001.png'> <mat:mi>G</mat:mi> </mat:math> <mat:mi xmlns:mat='http://www.w3.org/1998/Math/MathML'>G</mat:mi>G ‐spaces and its applications

Jüstel Dominik

摘要

Abstract > The Zak transform on <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0003" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12097-math-0003.png"> <mat:msup> <mat:mrow> <mat:mi mathvariant="double-struck">R</mat:mi> </mat:mrow> <mat:mi>d</mat:mi> </mat:msup> </mat:math> is an important tool in condensed matter physics, signal processing, time‐frequency analysis, and harmonic analysis in general. This article introduces a generalization of the Zak transform to a class of locally compact <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0004" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12097-math-0004.png"> <mat:mi>G</mat:mi> </mat:math> ‐spaces, where <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0005" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12097-math-0005.png"> <mat:mi>G</mat:mi> </mat:math> is either a locally compact abelian or a second countable unimodular type I group. This framework unifies previously proposed generalizations of the Zak transform. It is shown that the Zak transform has invariance properties analog to the classic case and is a Hilbert space isomorphism between the space of <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0006" xmlns:wiley="http://www.wil </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”xml：lang =“en”> <title type =“main”>抽象</ title> > zak转换在<mat：math xmlns：mat =“http://www.w3.org/1998/math/mathml”display =“内联”altimg =“urn：x-wiley：00246107：媒体：jlms12097：jlms12097-数学-0003“XMLNS：Wiley =”http://www.wiley.com/namespaces/wiley/wiley“wiley：location =”等式/ jlms12097-math-0003.png“> <mat：msup> <may：mrow> <mat：mi mathvariant =“双击”> r </ mat：mi> </ mat：mrow> <mat：mi> d </ mat：mi> </ mat：msup> </ mat：math>是一般凝聚物理学，信号处理，时频分析和谐波分析的重要工具。本文介绍了ZAK变换到一类当地紧凑的<MAT：MATH XMLNS：MAT =“http://www.w3.org/1998/math/mathml”display =“Inline”Altimg =“URN： X-Wiley：00246107：媒体：JLMS12097：JLMS12097-Math-0004“XMLNS：Wiley =”http://www.wiley.com/namespaces/wiley/wiley“wiley：location =”等式/ jlms12097-math-0004。 PNG“> <MAT：MI> G </ MAT：MI> </ MAT：MATH> - 空间，其中<MAT：MATH XMLNS：MAT =”http://www.w3.org/1998/math/mathml“ display =“内联”Altimg =“URN：X-Wiley：00246107：媒体：jlms12097：jlms12097-math-0005”xmlns：wiley =“http://www.wiley.com/namespaces/wiley/wiley”wiley：location =“等式/ jlms12097-math-0005.png”> <mat：mi> g </ mat：mi> </ mat：math>是局部紧凑的abelian或第二个可数单模I型组。该框架统一了先前提出的ZAK变换的概括。结果表明，Zak变换具有不变性的属性模拟与经典案例，是<mat：math xmlns：mat =“http://www.w3.org/1998/math/mathml”的空间之间的希尔伯特空间同构。显示=“内联”Altimg =“URN：X-Wiley：00246107：媒体：JLMS12097：JLMS12097-Math-0006”XMLNS：Wiley =“http：//www.wil </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>2018年第1期</span><b style="margin: 0 2px;">|</b><span>共30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=Jüstel Dominik&option=202" target="_blank" rel="nofollow">Jüstel Dominik;</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>Department of MathematicsTechnical University of MunichBoltzmannstr. 3 D‐85747 Garching near Munich Germany;</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=43A32 (primary)&option=203" rel="nofollow">43A32 (primary);</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=58D19&option=203" rel="nofollow">58D19;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=28C15 (secondary)&option=203" rel="nofollow">28C15 (secondary);</a> </p> <div class="translation"> 机译：43a32（初级）;58d19;28c15（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> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704024866789.html">The Zak transform on strongly proper <mat:math xmlns:mat="http://www.w3.org/1998/Math/MathML" display="inline" altimg="urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0001" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" wiley:location="equation/jlms12097-math-0001.png"> <mat:mi>G</mat:mi> </mat:math> <mat:mi xmlns:mat="http://www.w3.org/1998/Math/MathML">G</mat:mi>G ‐spaces and its applications</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Jüstel Dominik&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Jüstel Dominik </a> <a href="/journal-foreign-31023/" target="_blank" rel="nofollow" class="tuijian_authcolor">The Journal of the London Mathematical Society .</a> <span>2018</span><span>,第1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：Zak转换强烈正确<mat：math xmlns：mat =“http://www.w3.org/1998/math/mathml”display =“内联”altimg =“urn：x-wiley：00246107：媒体：jlms12097 ：JLMS12097-Math-0001“XMLNS：Wiley =”http://www.wiley.com/namespaces/wiley/wiley“wiley：location =”等式/ jlms12097-math-0001.png“> <mat：mi> g </ mat：mi> </ mat：math> <mat：mi xmlns：mat =“http://www.w3.org/1998/math/mathml”> g </ mat：mi> g - 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Wang </a> <span>2011</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：σ和<MML：数学altimg = “si1.gif” 溢出= “滚动” 的xmlns：xocs = “http://www.elsevier.com/xml/xocs/dtd” 的xmlns：XS =“HTTP：// WWW。 w3.org/2001/XMLSchema”的xmlns：的xsi = “http://www.w3.org/2001/XMLSchema-instance” 的xmlns = “http://www.elsevier.com/xml/ja/dtd” 的xmlns： JA = “http://www.elsevier.com/xml/ja/dtd” 的xmlns：MML = “http://www.w3.org/1998/Math/MathML” 的xmlns：TB =“HTTP：// WWW .elsevier.com / XML /普通/表/ DTD “的xmlns：SB = ”http://www.elsevier.com/xml/common/struct-bib/dtd“ 的xmlns：CE =” HTTP：//www.elsevier的.com / XML /普通/ DTD “的xmlns：的xlink = ”http://www.w3.org/1999/xlink“ 的xmlns：CALS =” http://www.elsevier.com/xml/common/cals/dtd “> <MML：MSUB> <MML：MI>˚F</ MML：MI> <MML：MN> 0 </ MML：MN> </ MML：MSUB> <MML：MO伸缩性=” 假“>（</ MML：MO> <MML：MN> 980 </ MML：MN> <MML：MO伸缩性= “假”>）</ MML：MO> </ MML：数学>从<MML子结构：数学altimg =“SI2。 GIF”溢出= “滚动” 的xmlns：xocs = “http://www.elsevier.com/xml/xocs/dtd” 的xmlns：XS = “http://www.w3.org/2001/XMLSchema” 的xmlns：的xsi = “http://www.w3.org/2001/XMLSchema-instance” 的xmlns =“HTTP：//www.elsevier。 COM / XML / JA / DTD”的xmlns：JA = “http://www.elsevier.com/xml/ja/dtd” 的xmlns：MML = “http://www.w3.org/1998/Math/MathML”的xmlns：TB = “http://www.elsevier.com/xml/common/table/dtd” 的xmlns：SB = “http://www.elsevier.com/xml/common/struct-bib/dtd” 的xmlns： CE = “http://www.elsevier.com/xml/common/dtd” 的xmlns：的xlink = “http://www.w3.org/1999/xlink” 的xmlns：CALS =“HTTP：//www.elsevier的.com / XML /普通/ CALS / DTD“> <MML：MI>γ</ MML：MI> <MML：MI>γ</ MML：MI> <MML：MO>→</ MML：MO> <MML ：MI>π</ MML：MI> <MML：MI>π</ MML：MI> </ MML：数学>，<MML：数学altimg = “si3.gif” 溢出= “滚动” 的xmlns：xocs =” http://www.elsevier.com/xml/xocs/dtd “的xmlns：XS = ”http://www.w3.org/2001/XMLSchema“ 的xmlns：的xsi =” http://www.w3.org/ 2001 / XMLSchema的实例”的xmlns = “http://www.elsevier.com/xml/ja/dtd” 的xmlns：JA = “http://www.elsevier.com/xml/ja/dtd” 的xmlns：MML = “http://www.w3.org/1998/Math/MathML” 的xmlns：TB = “http://www.elsevier.com/xml/common/table/dtd” 的xmlns：SB =“HTTP：// WWW .elsevier.com / XML /普通/结构-围兜/ DTD “的xmlns：CE = ”http://www.elsevier.com/xml/common/dtd“ 的xmlns：的xlink =” HTTP：//www.w 3.org/1999/xlink”的xmlns：CALS = “http://www.elsevier.com/xml/common/cals/dtd”> <MML：MI>Ĵ</ MML：MI> <MML：MO =伸缩性“假”> / </ MML：MO> <MML：MI>ψ</ MML：MI> <MML：MO>，</ MML：MO> <MML：MI>φ</ MML：MI> </ MML ：数学>辐射和<MML：数学altimg = “si4.gif” 溢出= “滚动” 的xmlns：xocs = “http://www.elsevier.com/xml/xocs/dtd” 的xmlns：XS =“HTTP：/ /www.w3.org/2001/XMLSchema “的xmlns：的xsi = ”http://www.w3.org/2001/XMLSchema-instance“ 的xmlns =” http://www.elsevier.com/xml/ja/dtd “的xmlns：JA =” http://www.elsevier.com/xml/ja/dtd “的xmlns：MML = ”http://www.w3.org/1998/Math/MathML“ 的xmlns：TB =” HTTP： //www.elsevier.com/xml/common/table/dtd “的xmlns：SB = ”http://www.elsevier.com/xml/common/struct-bib/dtd“ 的xmlns：CE =” HTTP：// 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transform on strongly proper <mat:math xmlns:mat='http://www.w3.org/1998/Math/MathML' display='inline' altimg='urn:x-wiley:00246107:media:jlms12097:jlms12097-math-0001' xmlns:wiley='http://www.wiley.com/namespaces/wiley/wiley' wiley:location='equation/jlms12097-math-0001.png'> <mat:mi>G</mat:mi> </mat:math> <mat:mi xmlns:mat='http://www.w3.org/1998/Math/MathML'>G</mat:mi>G ‐spaces and its applications" data-price="20" data-site-name="" data-transnum="24" style="display:none;"></span> <input type="hidden" value="4" id="sourcetype"> <input type="hidden" value="31023" id="journalid"> <input type="hidden" value="1" id="inyn_provide_service_level"> <input type="hidden" value="https://cdn.zhangqiaokeyan.com" id="imgcdn"> <input type="hidden" value="1" id="isdeatail"> <input type="hidden" value="" id="syyn_indexed_database"> <input type="hidden" value="" id="servicetype"> <input type="hidden" id="pagename" value="The Zak transform on strongly proper <mat:math 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The Zak transform on strongly proper G GG ‐spaces and its applications

摘要