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可靠群理论——介绍抽象调和分析的一个方向
An Introduction to the Theory of Amenable Groups——One of the Approaches to the Abstract Harmonic Analysis

袁传宽
Yuan Chuankuan

清华大学
(Department of Appliei, Mathematics,Tsinghua University

收稿日期: 1989-12-25
出版日期: 1989-10-15

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摘要  一、可靠群的研究背景 三十年代,von Danzig与Freudenthal在拓扑群的研究中做了开创性工作.在同一时代,Haar,von Neumann以及Weil又分别在可分局部紧致群与一般局部紧致群上确定了单边平移不变的测度,亦即我们现在说的左Haar测度.所有这一切为抽象调和分析或局部紧致群上的调和分析提供了基石.抽象调和分析的研究出现了许多令人瞩目的方向.近三十年来,有关可靠群(E:amenable group;F:groupe moyennable;G:mittebare gruppe;R:)的研究就是其中之一.
Abstract:As the Harmonic Analysis on locally compact abelian groups has been getting well developed, more and more mathematicians have been attracted to the more natural but difficult topic of Harmonic Analysis on arbitrary locally compact groups. So to speak, one of the successful approaches to this hard subject is trying to establish the harmonic analysis on amenable locally compact groups.This paper is an introduction to the theory of amenable groups, its historical origin and its most important developments in the recent three decades.
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