与超几何 Gabor 变换相关的托普利兹算子及其应用

IF 0.7 4区数学 Q2 MATHEMATICS

Complex Analysis and Operator Theory Pub Date : 2024-07-01 DOI:10.1007/s11785-024-01569-3

Hatem Mejjaoli

{"title":"与超几何 Gabor 变换相关的托普利兹算子及其应用","authors":"Hatem Mejjaoli","doi":"10.1007/s11785-024-01569-3","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce and we study the hypergeometric Gabor transform attached to the Cherednik operators in the W-invariant case. We investigate for this transform the main theorems of Harmonic analysis. The theory of the reproducing kernel Hilbert spaces has relatively recent developments in pure and applied mathematics. Motivated by Wong’s approach and involving the theory of RKHS, we introduce, study and giving some applications on the Toeplitz operators associated with the hypergeometric Gabor transform. Results on the \\(L^{p}\\)-boundedness and \\(L^{p}\\)-compactness of these Toeplitz operators are also given.","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":"15 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Toeplitz Operators Associated with the Hypergeometric Gabor Transform and Applications\",\"authors\":\"Hatem Mejjaoli\",\"doi\":\"10.1007/s11785-024-01569-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce and we study the hypergeometric Gabor transform attached to the Cherednik operators in the W-invariant case. We investigate for this transform the main theorems of Harmonic analysis. The theory of the reproducing kernel Hilbert spaces has relatively recent developments in pure and applied mathematics. Motivated by Wong’s approach and involving the theory of RKHS, we introduce, study and giving some applications on the Toeplitz operators associated with the hypergeometric Gabor transform. Results on the \\\\(L^{p}\\\\)-boundedness and \\\\(L^{p}\\\\)-compactness of these Toeplitz operators are also given.\",\"PeriodicalId\":50654,\"journal\":{\"name\":\"Complex Analysis and Operator Theory\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Analysis and Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-024-01569-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01569-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们介绍并研究了在 W 不变情况下 Cherednik 算子所附带的超几何 Gabor 变换。我们针对这一变换研究了谐波分析的主要定理。重现核希尔伯特空间理论在纯数学和应用数学中的发展相对较晚。受黄氏方法的启发并涉及 RKHS 理论，我们介绍、研究了与超几何 Gabor 变换相关的 Toeplitz 算子，并给出了一些应用。我们还给出了这些托普利兹算子的有界性和\(L^{p}\)紧凑性的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Toeplitz Operators Associated with the Hypergeometric Gabor Transform and Applications

In this paper, we introduce and we study the hypergeometric Gabor transform attached to the Cherednik operators in the W-invariant case. We investigate for this transform the main theorems of Harmonic analysis. The theory of the reproducing kernel Hilbert spaces has relatively recent developments in pure and applied mathematics. Motivated by Wong’s approach and involving the theory of RKHS, we introduce, study and giving some applications on the Toeplitz operators associated with the hypergeometric Gabor transform. Results on the \(L^{p}\)-boundedness and \(L^{p}\)-compactness of these Toeplitz operators are also given.

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

Complex Analysis and Operator Theory 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

107

审稿时长

3 months

期刊介绍： Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.