On the zero sets of the Fourier transform of singular measures
type: Item
instance of: scholarly article
title: On the zero sets of the Fourier transform of singular measures
zbMATH Open document ID: 1413.42010
author: Erdal Karapınar
published in: Analysis Mathematica
publication date: 2019-02-01T00:00:00Z
review text: The author shows that the class of sets \(E\) with the property that there exists a measure singular with respect to the Lebesgue measure whose Fourier transform tends to 0 at infinity and vanishes on \(E\) contains the Helson sets. He calls \(E \subset \mathbb R\) a \(\theta\)-set iff for every \(g\in C0(E)\) there exists a singular measure \(\mu\in M(R)\) such that \(\mu(t) = g(t)\) for \(t\in E\). The main result is: The class of Helson sets coincides with the class of \(\theta\)-sets. He shows that the class of sets \(E\) with the property that there exists a measure singular with respect to the Lebesgue measure whose Fourier transform tends to 0 at infinity and vanishes on \(E\) contains the Helson sets.
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 7011046
zbMATH Keywords: singular measure
zbMATH Keywords: special set
reviewed by: Antonio López-Carmona
MaRDI profile type: Publication
full work available at URL: s10476-018-0507-3
OpenAlex ID: W2891052868
DOI: 10.1007/S10476-018-0507-3
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description: scientific article; zbMATH DE number 7011046