Concentration functions in locally compact groups
type: Item
instance of: scholarly article
title: Concentration functions in locally compact groups
zbMATH Open document ID: 0854.43001
DOI: 10.1007/BF01444244
author: Wojciech Jaworski
author: J. Rosenblatt
author: George A. Willis
published in: Mathematische Annalen
publication date: 1997-01-07T00:00:00Z
full work available at URL: https://eudml.org/doc/183010
review text: This article gives various theorems describing when the concentration functions of a probability measure on a locally compact Hausdorff group converge to 0. In the first section, this is proved assuming that the measure is irreducible, thereby giving a positive solution of the Hofmann-Mukherjea problem. In the second section, the same result is again proved for general groups, but with the assumption that the probability measure is adapted and almost aperiodic. The non-existence of strange locally compact groups is central to both of these results. In the third section, general issues connected with the concentration function problem and a possible representation theoretic approach are discussed.
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 60B10
zbMATH DE Number: 932003
zbMATH Keywords: concentration functions
zbMATH Keywords: probability measure
zbMATH Keywords: locally compact Hausdorff group
zbMATH Keywords: Hofmann-Mukherjea problem
zbMATH Keywords: representation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 932003