Strong characterizing sequences for subgroups of compact groups
type: Item
instance of: scholarly article
title: Strong characterizing sequences for subgroups of compact groups
zbMATH Open document ID: 1153.11031
author: András Biró
published in: Journal of Number Theory
publication date: 2007-01-26T00:00:00Z
review text: For a finitely generated subgroup \(\Gamma\) of a compact metrizable Abelian group \(G\) it is shown that there is a subset \(A\) of the dual group \(G^*\) of \(G\) such that \(\gamma\in\Gamma\) iff \(\sum_{a\in A}\nu(\| a\gamma\|)<\infty\). Here \(\nu\) is a weight function and \(\| x\| \) denotes the distance of \(x\) to the nearest integer. This was proved in [\textit{A. Biró} and \textit{V. T. Sós}, J. Number Theory 99, No. 2, 405--414 (2003; Zbl 1058.11047)] for the torus group. Conditions for different weight functions \(\nu\) are given, which guarantee that there is \(A\subset G^*\) which yield characterizing sequences of the above type for both weight functions.
Mathematics Subject Classification ID: 11J13
Mathematics Subject Classification ID: 22B99
zbMATH DE Number: 5118764
zbMATH Keywords: Strong characterizing sequence
zbMATH Keywords: Compact Abelian group
zbMATH Keywords: Subgroup
MaRDI profile type: Publication
full work available at URL: j.jnt.2006.03.008
OpenAlex ID: W2057397446
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DOI: 10.1016/J.JNT.2006.03.008
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description: scientific article; zbMATH DE number 5118764