On the convergence in category of trigonometric series
type: Item
instance of: scholarly article
title: On the convergence in category of trigonometric series
zbMATH Open document ID: 0814.42005
DOI: 10.1007/BF02844623
publication date: 1994-08-22T00:00:00Z
review text: The main result of the paper is the following theorem related to the classical theorem of Menchoff: If \(f\) is a continuous function on \([- \pi,\pi]\), then for each \(\varepsilon> 0\) there exists a set \(X\) of second category such that \(m([-\pi,\pi]- X)<\varepsilon\) and a trigonometric series which converges to \(f\) on \(X\) has uniformly bounded partial sums. The result cannot be improved to obtain a set of full measure.
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 40A05
zbMATH DE Number: 604862
zbMATH Keywords: convergence in category
zbMATH Keywords: theorem of Menchoff
zbMATH Keywords: trigonometric series
author: V. Aversa
author: Alexander Olevskiĭ
reviewed by: Władysław Wilczyński
MaRDI profile type: Publication
cites work: Q5338374
cites work: On convergence and growth of partial sums of Fourier series
cites work: A category analogue of the density topology
cites work: Q3913627
full work available at URL: https://doi.org/10.1007/bf02844623
OpenAlex ID: W2046944803
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 604862