Cayley 图上加权拉普拉斯算子的通用谱

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-06-04 DOI:10.1007/s11005-024-01827-7

Cristian F. Coletti, Lucas R. de Lima, Diego S. de Oliveira, Marcus A. M. Marrocos

{"title":"Cayley 图上加权拉普拉斯算子的通用谱","authors":"Cristian F. Coletti, Lucas R. de Lima, Diego S. de Oliveira, Marcus A. M. Marrocos","doi":"10.1007/s11005-024-01827-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01827-7.pdf","citationCount":"0","resultStr":"{\"title\":\"Generic spectrum of the weighted Laplacian operator on Cayley graphs\",\"authors\":\"Cristian F. Coletti, Lucas R. de Lima, Diego S. de Oliveira, Marcus A. M. Marrocos\",\"doi\":\"10.1007/s11005-024-01827-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds.</p></div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":\"114 3\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11005-024-01827-7.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01827-7\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01827-7","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们研究了 Cayley 图上一类加权拉普拉斯的谱，并确定了在什么条件下相应的特征空间一般是不可还原的。具体来说，我们分析了具有不变度量的左不变 Cayley 图上的谱，并给出了一般不可还原特征空间的一些标准。此外，我们还引入了一个可与拉普拉奇相提并论的算子，并证明同样的标准成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Generic spectrum of the weighted Laplacian operator on Cayley graphs

查看原文本刊更多论文

Generic spectrum of the weighted Laplacian operator on Cayley graphs

In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on left-invariant Cayley graphs endowed with an invariant metric, and we give some criteria for generically irreducible eigenspaces. Additionally, we introduce an operator that is comparable to the Laplacian and show that the same criterion holds.

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

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.