Behavior of divergent Haar series
type: Item
instance of: scholarly article
title: Behavior of divergent Haar series
zbMATH Open document ID: 0581.42002
DOI: 10.1007/BF01156463
published in: Mathematical Notes
publication date: 1984-01-01T00:00:00Z
review text: The main result is the following: Let the series (*) \(\sum^{\infty}_{n=1} a_{i_ n}\chi_{i_ n}(x)\) be obtained as the result of an arbitrary permutation of the Haar series \(\sum^{\infty}_{n=1}a_ n\chi (x)\), satisfying \(a_ n\chi_ n(x)=o(n)\). Then on any interval \((\alpha,\beta)\subset [0,1]\) one can find a continuum of points at which (*) converges either to a finite value or to infinity of specific sign. This result is true, in particular, for Fourier-Haar series.
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 3929633
zbMATH Keywords: Haar series
zbMATH Keywords: Fourier-Haar series
author: Valentin Skvortsov
reviewed by: Babban Prasad Mishra
MaRDI profile type: Publication
cites work: Some generalizations of uniqueness theorems for series in Walsh systems
cites work: Q5574798
cites work: Q4112399
full work available at URL: https://doi.org/10.1007/bf01156463
OpenAlex ID: W2051902935
description: scientific article; zbMATH DE number 3929633