\(M\)-sets and measures
type: Item
instance of: scholarly article
title: \(M\)-sets and measures
zbMATH Open document ID: 0793.42006
DOI: 10.2307/2946565
author: Robert Kaufman
published in: Annals of Mathematics. Second Series
publication date: 1992-09-26T00:00:00Z
review text: A theorem of \textit{R. Lyons} [Ann. Math., II. Ser. 122, 155-170 (1985; Zbl 0583.43006)] states that a measure on the circle group has Fourier- Stieltjes coefficients not tending to 0 iff it has positive mass on some (closed) \(U_ 0\)-set (set of uniqueness in the wide sense). The author answers the outstanding question whether the above theorem can be restated with \(U\)-sets (sets of uniqueness) instead of \(U_ 0\)-sets in the negative by constructing a measure \(\mu\) whose Fourier-Stieltjes coefficients do not tend to 0, but still vanishes on all sets of uniqueness, i.e., the only closed sets of positive \(\mu\)-measure are \(M\)- sets (sets of multiplicity).
Mathematics Subject Classification ID: 42A63
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 55726
zbMATH Keywords: \(M\)-sets
zbMATH Keywords: sets of uniqueness
zbMATH Keywords: sets of multiplicity
zbMATH Keywords: Fourier-Stieltjes coefficients
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2946565
OpenAlex ID: W2318286090
description: scientific article; zbMATH DE number 55726