Divergence of Fourier-Haar series of bounded functions on sets of measure zero
type: Item
instance of: scholarly article
title: Divergence of Fourier-Haar series of bounded functions on sets of measure zero
zbMATH Open document ID: 0801.42020
DOI: 10.1007/BF01262173
author: V. M. Bugadze
published in: Mathematical Notes
publication date: 1994-04-12T00:00:00Z
review text: Answering a question posed by the reviewer [Colloq. Math. 52, 213-238 (1987; Zbl 0642.42024)] the author proves that given a set \(E \subseteq [0,1]\) of Lebesgue measure zero, there is a bounded measurable function \(f\) on \([0,1]\) whose Haar-Fourier series diverges everywhere on \(E\). The construction is based on a clever iterative procedure which generates a sequence of nested \(G_ \delta\) sets (whose components are dyadic intervals) which approximate \(E\). These sets are used to define \(f\) and to control the size of each term of the Haar-Fourier series of \(f\) at points on \(E\).
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 525666
zbMATH Keywords: Haar-Fourier series
zbMATH Keywords: dyadic intervals
reviewed by: William R. Wade
MaRDI profile type: Publication
cites work: Sur les ensembles de divergence des séries trigonométriques
cites work: Unbounded divergence of Fourier series of continuous functions
cites work: Recent developments in the theory of Haar series
cites work: Q5722351
cites work: Q4112399
description: scientific article; zbMATH DE number 525666