Decreasing rearranged Fourier series
type: Item
instance of: scholarly article
title: Decreasing rearranged Fourier series
zbMATH Open document ID: 0978.42004
DOI: 10.1007/BF01274186
published in: The Journal of Fourier Analysis and Applications
publication date: 2001-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/59594
review text: In a previous paper, the author proved that there exists a real \(f\in L^2(T)\) whose Fourier sum, when taken in decreasing order of magnitude of the coefficients, diverges unboundedly almost everywhere. In the present paper this result is improved by taking \(f\) continuous. The proof follows the general lines of the former theorem but is substantially more intricate. The key new ingredients are a result of Kahane, establishing control over the size of the coefficients and the amplitude of certain trigonometric polynomials and a modified Olevskij lemma. In spite of the fact that the methods used in this paper are baroque (with the author's own word) this paper is remarkable, among others by the interesting comments covering the different steps of the proof.
reviewed by: Rupert Lasser
Mathematics Subject Classification ID: 42A20
Mathematics Subject Classification ID: 42C20
zbMATH DE Number: 1275884
zbMATH Keywords: divergence
zbMATH Keywords: Fourier series
zbMATH Keywords: rearrangement
author: T. W. Körner
MaRDI profile type: Publication
cites work: Q5538132
cites work: Sur Les Polynomes a Coefficients Unimodulaires
cites work: Divergence of decreasing rearranged Fourier series
cites work: Q4084169
cites work: Q5641810
cites work: On the almost everywhere convergence of wavelet summation methods
OpenAlex ID: W2074442574
description: scientific article; zbMATH DE number 1275884