与 (κ,n)-Fourier 变换相关的 Titchmarsh 和 Boas 型定理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-03 DOI:10.1515/anly-2023-0045

Mehrez Mannai, S. Negzaoui

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引用次数: 0

摘要

摘要本文旨在证明 Titchmarsh 定理对广义傅里叶变换 ( κ , n {\kappa,n} )-Fourier 变换的推广，其中 n 为正整数，κ 为来自 Dunkl 理论的常数。作为应用，我们推导出 L 2 {L^{2}} 的 ( κ , n ) {(\kappa,n)} - 傅立叶乘数定理。Lipschitz 空间的傅里叶乘数定理。此外，我们给出了必要条件，以确保 f 属于阶数为 m 的广义 Lipschitz 类中的任意一类。这使得我们可以为 ℱ κ , n {\mathcal{F}_{\kappa,n}} 建立类似的 Boas 型结果。.

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Titchmarsh and Boas-type theorems related to (κ,n)-Fourier transform

Abstract The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called ( κ , n {\kappa,n} )-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a ( κ , n ) {(\kappa,n)} -Fourier multiplier theorem for L 2 {L^{2}} Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for ℱ κ , n {\mathcal{F}_{\kappa,n}} .

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.