利用分数傅立叶变换刻画回转器变换

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2022-11-04 DOI:10.1080/10652469.2022.2138868

T. Kagawa, Toshio Suzuki

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引用次数: 0

摘要

摘要在本文中，我们将解释分数傅立叶变换和回转器变换之间的关系。特别地，我们将展示回转器变换的性质，即得到回转器变换本征函数和本征值，递归公式，Wigner分布与回转器变换之间的关系，满足某些函数的回转器变换所需的微分方程，以及回转器变换作为自伴算子的表示。此外，我们将考虑回火分布的广义回转器变换。

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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Characterizations of the gyrator transform via the fractional Fourier transform

ABSTRACT In this note, we will explain the relationship between the fractional Fourier transform and the gyrator transform. In particular, we will show the properties of the gyrator transform, which is getting the eigenfunction and eigenvalue of the gyrator transform, recursion formula, the relation between the Wigner distribution and the gyrator transform, the differential equation satisfied with the gyrator transform of some functions, and the representation of the gyrator transform as the self-adjoint operator. Moreover, we will consider the generalized gyrator transform of tempered distributions.

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来源期刊

Integral Transforms and Special Functions 数学-数学

CiteScore

2.20

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Integral Transforms and Special Functions belongs to the basic subjects of mathematical analysis, the theory of differential and integral equations, approximation theory, and to many other areas of pure and applied mathematics. Although centuries old, these subjects are under intense development, for use in pure and applied mathematics, physics, engineering and computer science. This stimulates continuous interest for researchers in these fields. The aim of Integral Transforms and Special Functions is to foster further growth by providing a means for the publication of important research on all aspects of the subjects.