邓克尔型西格尔-巴格曼变换的普朗切尔公式和反演公式

Q2 Mathematics

Annali dell''Universita di Ferrara Pub Date : 2024-11-14 DOI:10.1007/s11565-024-00563-z

Fethi Soltani, Meriem Nenni

{"title":"邓克尔型西格尔-巴格曼变换的普朗切尔公式和反演公式","authors":"Fethi Soltani, Meriem Nenni","doi":"10.1007/s11565-024-00563-z","DOIUrl":null,"url":null,"abstract":"<div><p>In 1961, Bargmann introduced the classical Segal-Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal-Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper we introduce the Dunkl-type Segal-Bargmann transform <span>\\(\\mathscr {B}_{\\alpha }\\)</span> associated with the Coxeter group <span>\\(\\mathbb {Z}^d_2\\)</span>. Next, we investigate for this transform the main theorems of harmonic analysis (Plancherel and inversion formulas). Finally, we study some local uncertainty principles associated with the transform <span>\\(\\mathscr {B}_{\\alpha }\\)</span>.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Plancherel and inversion formulas for the Dunkl-type Segal-Bargmann transform\",\"authors\":\"Fethi Soltani, Meriem Nenni\",\"doi\":\"10.1007/s11565-024-00563-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In 1961, Bargmann introduced the classical Segal-Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal-Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper we introduce the Dunkl-type Segal-Bargmann transform <span>\\\\(\\\\mathscr {B}_{\\\\alpha }\\\\)</span> associated with the Coxeter group <span>\\\\(\\\\mathbb {Z}^d_2\\\\)</span>. Next, we investigate for this transform the main theorems of harmonic analysis (Plancherel and inversion formulas). Finally, we study some local uncertainty principles associated with the transform <span>\\\\(\\\\mathscr {B}_{\\\\alpha }\\\\)</span>.</p></div>\",\"PeriodicalId\":35009,\"journal\":{\"name\":\"Annali dell''Universita di Ferrara\",\"volume\":\"71 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annali dell''Universita di Ferrara\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11565-024-00563-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annali dell''Universita di Ferrara","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s11565-024-00563-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

1961 年，Bargmann 提出了经典的 Segal-Bargmann 变换，1984 年，Cholewinsky 提出了广义的 Segal-Bargmann 变换。这两种变换是许多著作的目标，在数学中有着广泛的应用。在本文中，我们介绍了与考克斯特群 \(\mathbb {Z}^d_2\) 相关的邓克尔型西格尔-巴格曼变换（Dunkl-type Segal-Bargmann transform \(\mathscr {B}_{\alpha }\）。接下来，我们将针对这一变换研究谐波分析的主要定理（Plancherel 和反演公式）。最后，我们研究与变换 \(\mathscr {B}_{\alpha }\) 相关的一些局部不确定性原理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Plancherel and inversion formulas for the Dunkl-type Segal-Bargmann transform

In 1961, Bargmann introduced the classical Segal-Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal-Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper we introduce the Dunkl-type Segal-Bargmann transform \(\mathscr {B}_{\alpha }\) associated with the Coxeter group \(\mathbb {Z}^d_2\). Next, we investigate for this transform the main theorems of harmonic analysis (Plancherel and inversion formulas). Finally, we study some local uncertainty principles associated with the transform \(\mathscr {B}_{\alpha }\).

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

Annali dell''Universita di Ferrara Mathematics-Mathematics (all)

CiteScore

1.70

自引率

0.00%

发文量

期刊介绍： Annali dell''Università di Ferrara is a general mathematical journal publishing high quality papers in all aspects of pure and applied mathematics. After a quick preliminary examination, potentially acceptable contributions will be judged by appropriate international referees. Original research papers are preferred, but well-written surveys on important subjects are also welcome.