A note on the growth of topological Sidon sets
type: Item
instance of: scholarly article
title: A note on the growth of topological Sidon sets
zbMATH Open document ID: 0853.43012
DOI: 10.1007/BF02837194
author: K. Gowri Navada
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-07-15T00:00:00Z
review text: Let \(G\) denote a locally compact abelian group and \(\Lambda\) a subset of the dual group. \(\Lambda\) is called a topological Sidon set if any bounded complex-valued function on \(\Lambda\) may be matched by the restriction to \(\Lambda\) of the Fourier transform of a complex bounded Radon measure \(\mu\) on \(G\). For any such \(\Lambda\) there exist \(c \geq 1\) and a compact subset \(K\) of \(G\) such that the measure \(\mu\) may be assumed to be supported on \(K\) and have norm at most \(c\) times the sup-norm of the associated bounded function on \(\Lambda\). The author gives standard estimates for the number of elements in the intersection of topological Sidon sets with compact convex subsets in \(\mathbb{R}^m\).
Mathematics Subject Classification ID: 43A46
zbMATH DE Number: 903362
zbMATH Keywords: locally compact abelian group
zbMATH Keywords: dual group
zbMATH Keywords: topological Sidon set
zbMATH Keywords: Fourier transform
zbMATH Keywords: Radon measure
MaRDI profile type: Publication
cites work: Q5685535
cites work: Arithmetic characterizations of Sidon sets
description: scientific article; zbMATH DE number 903362