Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform

IF 0.7 3区数学 Q2 MATHEMATICS

Integral Transforms and Special Functions Pub Date : 2023-02-13 DOI:10.1080/10652469.2023.2176488

F. Soltani, Hanen Saadi

引用次数: 1

Abstract

In 1961, Bargmann introduced the classical Segal–Bargmann transform and in 1984, Cholewinsky introduced the generalized Segal–Bargmann transform. These two transforms are the aim of many works, and have many applications in mathematics. In this paper, we introduce the Weinstein-type Segal–Bargmann transform ; and we prove for this transform Plancherel and inversion formulas. Next, we give a relation between the transform and the Weinstein transform in . As applications, we establish a local-type uncertainty inequalities (two versions) and a dispersion inequality for .

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weinstein型Segal-Bargmann变换的反演公式和不确定性不等式

1961年，Bargmann引入了经典的Segal–Bargmann变换，1984年，Cholewinsky引入了广义Segal–Balgmann变换。这两种变换是许多著作的目的，在数学中有许多应用。在本文中，我们引入了Weinstein型Segal–Bargmann变换；并证明了该变换的Plancherel和反演公式。接下来，我们给出了中的变换和Weinstein变换之间的关系。作为应用，我们建立了的局部型不确定性不等式（两个版本）和离散不等式。

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

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.