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arXiv · 1003.5747

Sur les séries de Fourier des fonctions continues unimodulaires

Jean Bourgain·Jean-Pierre Kahane
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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.

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Jean Bourgain, Jean-Pierre Kahane. 2010-03-30. Sur les séries de Fourier des fonctions continues unimodulaires. https://arxiv.org/abs/1003.5747

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