连通半简单李群的不确定性原理推广

IF 0.5 Q3 MATHEMATICS Asian-European Journal of Mathematics Pub Date : 2023-11-10 DOI:10.1142/s1793557123502303

Mykola Yaremenko

{"title":"连通半简单李群的不确定性原理推广","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":"{\"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}","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

摘要

在本文中，我们建立了Hardy定理的广义变式，即对于[公式:见文]一个可分离Hilbert空间，[公式:见文]一个具有Haar测度的连通半简单李群，[公式:见文]中[公式:见文]的一个酉表示，[公式:见文]上[公式:见文]的一个对偶测度，如果不等式[公式:见文]和[公式:见文]对[公式:见文]成立，则函数[公式:见文]几乎对所有[公式:见文本]都必须等于零。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The uncertainty principle generalization for a connected semi-simple Lie group

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].

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

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.

期刊最新文献

Billingsley type theorem of Bowen polynomial entropy for fixed-point free flows Graded quasi-S-primary ideals Probabilistic analysis and optimization of search algorithms Matrix representations of linear transformations on bicomplex space On static perfect fluid spacetimes and almost co-Kahler manifolds