Linear Canonical Space-Time Transform and Convolution Theorems

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2025-05-21 DOI:10.1007/s00006-025-01386-7

Yi-Qiao Xu, Bing-Zhao Li

引用次数: 0

Abstract

Following the idea of the fractional space-time Fourier transform, a linear canonical space-time transform for 16-dimensional space-time \(C\ell _{3,1}\)-valued signals is investigated in this paper. First, the definition of the proposed linear canonical space-time transform is given, and some related properties of this transform are obtained. Second, the convolution operator and the corresponding convolution theorem are proposed. Third, the convolution theorem associated with the two-sided linear canonical space-time transform is derived.

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线性正则时空变换与卷积定理

本文根据分数阶时空傅里叶变换的思想，研究了16维时空\(C\ell _{3,1}\)值信号的线性正则时空变换。首先，给出了所提出的线性正则时空变换的定义，并得到了该变换的一些相关性质。其次，给出了卷积算子及其相应的卷积定理；第三，推导了与双侧线性正则时空变换相关的卷积定理。

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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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.