{"title":"Inversion formula and uncertainty inequalities for the Weinstein-type Segal–Bargmann transform","authors":"F. Soltani, Hanen Saadi","doi":"10.1080/10652469.2023.2176488","DOIUrl":null,"url":null,"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 .","PeriodicalId":54972,"journal":{"name":"Integral Transforms and Special Functions","volume":"34 1","pages":"619 - 634"},"PeriodicalIF":0.7000,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Transforms and Special Functions","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10652469.2023.2176488","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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 .
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.
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