Jacques Peyrière et les produits de Riesz

Jean-Pierre Kahane (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

Jacques Peyrière investigated Riesz products associated with a given set of frequencies and the corresponding coefficients : mutual singularity or absolute continuity of the measures defined by two such products, Hausdorff dimensions of the sets carrying such measures, multifractal analysis. The present expository paper starts from Peyrière's results and give some new ways to investigate the same questions. Since Riesz products are also an essential tool for Sidon sets, the characterisations of Sidon sets by Pisier and Bourgain, using quasi-independent sets, are given and commented. The paper ends with an elementary construction of a « big » quasi-independent set. The paper is in French. An introduction, in English, explains why it will not be published in the book to which it was intended to contribute.

Mots clés: Riesz products; Sidon sets; quasi-independent sets

Domaines: Analyse classique [math.CA]

Jean-Pierre Kahane. Jacques Peyrière et les produits de Riesz. 2009. ⟨hal-00466558⟩