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Abstract: Jacques Peyri\`ere investigated Riesz products associated with a given set offrequencies and the corresponding coefficients : mutual singularity or absolutecontinuity of the measures defined by two such products, Hausdorff dimensionsof the sets carrying such measures, multifractal analysis. The presentexpository paper starts from Peyri\`ere-s results and give some new ways toinvestigate the same questions. Since Riesz products are also an essential toolfor Sidon sets, the characterisations of Sidon sets by Pisier and Bourgain,using quasi-independent sets, are given and commented. The paper ends with anelementary construction of a <> quasi-independent set. The paper is inFrench. An introduction, in English, explains why it will not be published inthe book to which it was intended to contribute.



Autor: Jean-Pierre Kahane LM-Orsay

Fuente: https://arxiv.org/







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