On the differences and sums of periodic measurable functions
type: Item
instance of: scholarly article
title: On the differences and sums of periodic measurable functions
zbMATH Open document ID: 0929.26002
DOI: 10.1023/A:1006533020966
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: Author constructs two measurable periodic functions such that their sums are continuous and unbounded. This gives a negative answer to the question from the article by \textit{M. Laczkovich} and \textit{Sz. Révész} [Acta Math. Hung. 54, No. 3/4, 329-341 (1989; Zbl 0725.26004)] whether if \(f\) is continuous and has a measurable \((\alpha_1,\dots,\alpha_n)\)-decomposition then it also has a continuous \((\alpha_1,\dots,\alpha_n)\)-decomposition. Recall that \(f=f_1+\dots+f_n \) is \((\alpha_1,\dots,\alpha_n)\)-decomposition of \(f\) if \(f_i\) is periodic modulo \(\alpha_i\) for every \(i=1,\dots,n\).
Mathematics Subject Classification ID: 26A15
Mathematics Subject Classification ID: 42A16
zbMATH DE Number: 1355168
zbMATH Keywords: periodic measurable function
zbMATH Keywords: Fourier series
zbMATH Keywords: pseudo Dirichlet set
author: Tamás Keleti
reviewed by: Katarina Janková
MaRDI profile type: Publication
full work available at URL: a:1006533020966
OpenAlex ID: W1714492982
description: scientific article; zbMATH DE number 1355168