Real Paley–Wiener theorems for the linear canonical Dunkl transform

IF 0.9 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-11-06 DOI:10.1007/s43034-025-00476-8

S. Umamaheswari, Sandeep Kumar Verma, Hatem Mejjaoli

引用次数: 0

Abstract

We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley–Wiener theorem for the linear canonical Dunkl transform. Further, we characterize the square-integrable function f whose linear canonical Dunkl transform of the function is supported in the polynomial domain. Finally, we develop the Boas-type Paley–Wiener theorem for the linear canonical Dunkl transform.

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线性正则Dunkl变换的真正Paley-Wiener定理

研究了与线性正则Dunkl变换相关的Sobolev空间，并探讨了线性正则Dunkl算子的一些性质。在这些结果的基础上，我们建立了线性正则Dunkl变换的实Paley-Wiener定理。进一步，我们刻画了平方可积函数f，该函数的线性正则Dunkl变换在多项式域中支持。最后，我们给出了线性正则Dunkl变换的boas型paly - wiener定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.