{"title":"The uncertainty principle generalization for a connected semi-simple Lie group","authors":"Mykola Yaremenko","doi":"10.1142/s1793557123502303","DOIUrl":null,"url":null,"abstract":"In this paper, we are establishing the generalized variant of the Hardy theorem, which states that for [Formula: see text] a separable Hilbert space, [Formula: see text] a connected semi-simple Lie group with a Haar measure [Formula: see text] a unitary representation of [Formula: see text] in [Formula: see text], and [Formula: see text] a dual measure on [Formula: see text], if inequalities [Formula: see text] and [Formula: see text] hold for [Formula: see text], then the function [Formula: see text] must equal zero almost for all [Formula: see text].","PeriodicalId":45737,"journal":{"name":"Asian-European Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian-European Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s1793557123502303","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we are establishing the generalized variant of the Hardy theorem, which states that for [Formula: see text] a separable Hilbert space, [Formula: see text] a connected semi-simple Lie group with a Haar measure [Formula: see text] a unitary representation of [Formula: see text] in [Formula: see text], and [Formula: see text] a dual measure on [Formula: see text], if inequalities [Formula: see text] and [Formula: see text] hold for [Formula: see text], then the function [Formula: see text] must equal zero almost for all [Formula: see text].
期刊介绍：
Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.
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