双侧四元数傅里叶变换和均匀 Lipschitz 空间的博厄斯类型结果

IF 0.7 4区数学 Q2 MATHEMATICS Complex Analysis and Operator Theory Pub Date : 2024-03-04 DOI:10.1007/s11785-024-01491-8

引用次数: 0

摘要

摘要对于四元数代数（{\mathbb {H}}\）和（f:\mathbb R^2\rightarrow {\mathbb {H}}\），我们考虑一个双面四元数傅里叶变换（\\widehat{f}\）。根据 $\widehat{f}$ 的行为给出了 f 属于广义均匀 Lipschitz 空间的必要条件和充分条件。

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Boas Type Results for Two-Sided Quaternion Fourier Transform and Uniform Lipschitz Spaces

Abstract

For the quaternion algebra ${\mathbb {H}}$ and $f:\mathbb R^2\rightarrow {\mathbb {H}}$ , we consider a two-sided quaternion Fourier transform $\widehat{f}$ . Necessary and sufficient conditions for f to belong to generalized uniform Lipschitz spaces are given in terms of behavior of $\widehat{f}$ .

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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.

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