Dual Boas Type Results for the Quaternion Transform and Generalized Lipschitz Spaces

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-10-14 DOI:10.1007/s00006-023-01301-y

Sergey Volosivets

引用次数: 0

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 \({\widehat{f}}\) to belong to generalized uniform Lipschitz spaces are given in terms of behavior of f.

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四元数变换与广义Lipschitz空间的对偶Boas型结果

对于四元数代数\（｛\mathbb｛H｝｝）和\（f:\mathbb R^2 \rightarrow｛\math bb｛H｝），我们考虑一个双边四元数傅立叶变换\（｝\widehat｛f｝）。根据f的性质，给出了\（｛\widehat｛f｝｝）属于广义一致Lipschitz空间的充要条件。

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

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.