Sur les s\'eries de Fourier des fonctions continues unimodulaires
Classical Analysis and ODEs
2010-03-31 v1
Abstract
The Fourier series of continuous functions of constant absolute value have interesting properties : according to the main theorems of the article, if the coefficients with positive indexes are square-summable with respect to a certain weight (any real positive power of the index), the same is true for negative indexes. The result extends to VMO and does not to bounded measurable functions.
Cite
@article{arxiv.1003.5747,
title = {Sur les s\'eries de Fourier des fonctions continues unimodulaires},
author = {Jean Bourgain and Jean-Pierre Kahane},
journal= {arXiv preprint arXiv:1003.5747},
year = {2010}
}
Comments
This article will appear soon in Ann. Inst. Fourier.