Uniqueness theorems for Walsh series under a strong condition
type: Item
instance of: scholarly article
title: Uniqueness theorems for Walsh series under a strong condition
zbMATH Open document ID: 0811.42007
DOI: 10.1007/BF01872092
author: V. Pereyra
published in: Acta Mathematica Hungarica
publication date: 1994-09-05T00:00:00Z
review text: The author examines sets of uniqueness for the class of Walsh series which satisfy \[ \sum^{2^{n-1}-1}_{k= 2^ n} a_ k w_ k(x)= o(1) \] uniformly in \(x\) as \(n\to \infty\). He proves a structural theorem (which shows that every \(H^{(1)}\)-set on the dyadic group is a set of uniqueness for this class), and proves that some sets of Haar measure zero and all sets of positive Haar measure on the dyadic group are sets of multiplicity (i.e., not sets of uniqueness) for this class.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 42C25
zbMATH DE Number: 633877
zbMATH Keywords: \(U\)-sets
zbMATH Keywords: \(M\)-sets
zbMATH Keywords: sets of uniqueness
zbMATH Keywords: Walsh series
zbMATH Keywords: dyadic group
zbMATH Keywords: Haar measure
zbMATH Keywords: sets of multiplicity
reviewed by: William R. Wade
MaRDI profile type: Publication
cites work: Q5338374
cites work: On the Walsh Functions
cites work: Sets of Uniqueness for the Group of Integers of a p-Series Field
cites work: Uniqueness and Quasi-Measures on the Group of Integers of A p-Series Field
cites work: On generalized uniqueness theorems for Walsh series
full work available at URL: https://doi.org/10.1007/bf01872092
OpenAlex ID: W2039140100
description: scientific article; zbMATH DE number 633877