Clifford代数中的Beurling定理

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-06-03 DOI:10.1007/s00006-023-01284-w

Othman Tyr, Radouan Daher

引用次数: 2

摘要

在本研究中，E.Hitzer引入的Clifford–傅立叶变换满足了一些类似于欧几里得傅立叶变换的不确定性原理。得到了Clifford–Fourier变换的Beurling–Hörmander定理的类似结果。作为Beurling定理的直接结果，还推导了不确定性原理的其他版本，如Hardy、Gelfand–Shilov和Cowling–Price定理。

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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Beurling’s Theorem in the Clifford Algebras

In this research, the Clifford–Fourier transform introduced by E. Hitzer, satisfies some uncertainty principles similar to the Euclidean Fourier transform. An analog of the Beurling–Hörmander’s theorem for the Clifford–Fourier transform is obtained. As a straightforward consequence of Beurling’s theorem, other versions of the uncertainty principle, such as the Hardy, Gelfand–Shilov and Cowling–Price theorems are also deduced.

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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.