具有片断连续符号的块托普利兹行列式的渐近论

IF 3.1 1区 数学 Q1 MATHEMATICS
Estelle Basor, Torsten Ehrhardt, Jani A. Virtanen
{"title":"具有片断连续符号的块托普利兹行列式的渐近论","authors":"Estelle Basor,&nbsp;Torsten Ehrhardt,&nbsp;Jani A. Virtanen","doi":"10.1002/cpa.22223","DOIUrl":null,"url":null,"abstract":"<p>We determine the asymptotics of the block Toeplitz determinants <span></span><math>\n <semantics>\n <mrow>\n <mo>det</mo>\n <msub>\n <mi>T</mi>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>ϕ</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\det T_n(\\phi)$</annotation>\n </semantics></math> as <span></span><math>\n <semantics>\n <mrow>\n <mi>n</mi>\n <mo>→</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$n\\rightarrow \\infty$</annotation>\n </semantics></math> for <span></span><math>\n <semantics>\n <mrow>\n <mi>N</mi>\n <mo>×</mo>\n <mi>N</mi>\n </mrow>\n <annotation>$N\\times N$</annotation>\n </semantics></math> matrix-valued piecewise continuous functions <span></span><math>\n <semantics>\n <mi>ϕ</mi>\n <annotation>$\\phi$</annotation>\n </semantics></math> with a finitely many jumps under mild additional conditions. In particular, we prove that\n\n </p>","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"78 1","pages":"120-160"},"PeriodicalIF":3.1000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22223","citationCount":"0","resultStr":"{\"title\":\"Asymptotics of block Toeplitz determinants with piecewise continuous symbols\",\"authors\":\"Estelle Basor,&nbsp;Torsten Ehrhardt,&nbsp;Jani A. Virtanen\",\"doi\":\"10.1002/cpa.22223\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We determine the asymptotics of the block Toeplitz determinants <span></span><math>\\n <semantics>\\n <mrow>\\n <mo>det</mo>\\n <msub>\\n <mi>T</mi>\\n <mi>n</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <mi>ϕ</mi>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\det T_n(\\\\phi)$</annotation>\\n </semantics></math> as <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>n</mi>\\n <mo>→</mo>\\n <mi>∞</mi>\\n </mrow>\\n <annotation>$n\\\\rightarrow \\\\infty$</annotation>\\n </semantics></math> for <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>N</mi>\\n <mo>×</mo>\\n <mi>N</mi>\\n </mrow>\\n <annotation>$N\\\\times N$</annotation>\\n </semantics></math> matrix-valued piecewise continuous functions <span></span><math>\\n <semantics>\\n <mi>ϕ</mi>\\n <annotation>$\\\\phi$</annotation>\\n </semantics></math> with a finitely many jumps under mild additional conditions. In particular, we prove that\\n\\n </p>\",\"PeriodicalId\":10601,\"journal\":{\"name\":\"Communications on Pure and Applied Mathematics\",\"volume\":\"78 1\",\"pages\":\"120-160\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2024-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cpa.22223\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications on Pure and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22223\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cpa.22223","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

在温和的附加条件下,我们确定了块托普利兹行列式的渐近线,如同具有有限次跳跃的矩阵值片断连续函数。特别是,我们证明了 , , 和 是取决于矩阵符号的常数,并在我们的主要结果中进行了描述。我们的方法基于托普利兹行列式的新局部定理、计算具有片断连续矩阵值符号的托普利兹算子的弗雷德霍姆指数的新方法以及其他算子理论方法。作为我们结果的一个应用,我们考虑了在量子自旋链模型的纠缠熵研究中出现的片断连续符号。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Asymptotics of block Toeplitz determinants with piecewise continuous symbols

Asymptotics of block Toeplitz determinants with piecewise continuous symbols

We determine the asymptotics of the block Toeplitz determinants det T n ( ϕ ) $\det T_n(\phi)$ as n $n\rightarrow \infty$ for N × N $N\times N$ matrix-valued piecewise continuous functions ϕ $\phi$ with a finitely many jumps under mild additional conditions. In particular, we prove that

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
6.70
自引率
3.30%
发文量
59
审稿时长
>12 weeks
期刊介绍: Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信