On coanalytic families of sets in harmonic analysis
type: Item
instance of: scholarly article
title: On coanalytic families of sets in harmonic analysis
zbMATH Open document ID: 0703.43005
author: Gilles Godefroy
published in: Illinois Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \(\Gamma\) be a countably infinite Abelian discrete group, and G its compact dual group. A subset \(\Lambda\) of \(\Gamma\) is called a Rosenthal set if any function in \(L^{\infty}(G)\) whose Fourier transform vanishes outside \(\Lambda\) belongs to C(G). It is shown that the family of Rosenthal subsets of \(\Gamma\) is a coanalytic non Borel subset of \(2^{\Gamma}\).
reviewed by: Gilles Godefroy
Mathematics Subject Classification ID: 43A46
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 4153184
zbMATH Keywords: infinite Abelian discrete group
zbMATH Keywords: compact dual group
zbMATH Keywords: Fourier transform
zbMATH Keywords: Rosenthal subsets
zbMATH Keywords: coanalytic non Borel subset
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4153184