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

IF 1.1 1区哲学 0 PHILOSOPHY

ANALYSIS 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

ANALYSIS PHILOSOPHY-

CiteScore

1.30

自引率

12.50%

发文量

期刊介绍： Analysis is the most established and esteemed forum in which to publish short discussions of topics in philosophy. Articles published in Analysis lend themselves to the presentation of cogent but brief arguments for substantive conclusions, and often give rise to discussions which continue over several interchanges. A wide range of topics are covered including: philosophical logic and philosophy of language, metaphysics, epistemology, philosophy of mind, and moral philosophy.