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

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

引用次数: 0

Abstract

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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与 (κ,n)-Fourier 变换有关的 Titchmarsh 和 Boas 型定理

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。.

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

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

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