附属于某些 m 阶无势李群的球面分析

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Fourier Analysis and Applications Pub Date : 2024-04-02 DOI:10.1007/s00041-024-10076-0

Silvina Campos, José García, Linda Saal

{"title":"附属于某些 m 阶无势李群的球面分析","authors":"Silvina Campos, José García, Linda Saal","doi":"10.1007/s00041-024-10076-0","DOIUrl":null,"url":null,"abstract":"We introduce a family of generalized Gelfand pairs \$(K_m,N_m)\$ where \$N_m\$ is an \$m+2\$-step nilpotent Lie group and \$K_m\$ is isomorphic to the 3-dimensional Heisenberg group. We develop the associated spherical analysis computing the set of the spherical distributions and we obtain some results on the algebra of \$K_m\$-invariant and left invariant differential operators on \$N_m\$.","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":"45 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Spherical Analysis Attached to Some m-Step Nilpotent Lie Group\",\"authors\":\"Silvina Campos, José García, Linda Saal\",\"doi\":\"10.1007/s00041-024-10076-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a family of generalized Gelfand pairs \\\$(K_m,N_m)\\\$ where \\\$N_m\\\$ is an \\\$m+2\\\$-step nilpotent Lie group and \\\$K_m\\\$ is isomorphic to the 3-dimensional Heisenberg group. We develop the associated spherical analysis computing the set of the spherical distributions and we obtain some results on the algebra of \\\$K_m\\\$-invariant and left invariant differential operators on \\\$N_m\\\$.\",\"PeriodicalId\":15993,\"journal\":{\"name\":\"Journal of Fourier Analysis and Applications\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fourier Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00041-024-10076-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fourier Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00041-024-10076-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了广义格尔方对族 $(K_m,N_m)$，其中 $N_m$ 是一个 $m+2$- 步零potent Lie 群，而 $K_m$ 与三维海森堡群同构。我们发展了计算球面分布集合的相关球面分析，并得到了一些关于 $K_m$ 上不变和左不变微分算子代数的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Spherical Analysis Attached to Some m-Step Nilpotent Lie Group

We introduce a family of generalized Gelfand pairs $(K_m,N_m)$ where $N_m$ is an $m+2$-step nilpotent Lie group and $K_m$ is isomorphic to the 3-dimensional Heisenberg group. We develop the associated spherical analysis computing the set of the spherical distributions and we obtain some results on the algebra of $K_m$-invariant and left invariant differential operators on $N_m$.

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

Journal of Fourier Analysis and Applications 数学-应用数学

CiteScore

2.10

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics. TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers. Areas of applications include the following: antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications

期刊最新文献

Hankel Matrices Acting on the Dirichlet Space Matrix Spherical Functions on Finite Groups Remarks on Frames from Projective Representations of Locally Compact Groups $$L^p(\mathbb {R}^d)$$ Boundedness for a Class of Nonstandard Singular Integral Operators Approximation by Subsequences of Matrix Transform Means of Some Two-Dimensional Rectangle Walsh–Fourier Series