Sur les séries de Fourier des fonctions continues unimodulaires

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.

arXiv commentThis article will appear soon in Ann. Inst. Fourier.