Covering the Large Spectrum and Generalized Riesz Products

Covering the Large Spectrum and Generalized Riesz Products

Chang’s Lemma is a widely employed result in additive combinatorics. It gives optimal bounds on the dimension of the large spectrum of probability distributions on nite abelian groups. In this note, we show how Chang’s Lemma and a powerful variant due to Bloom both follow easily from an approximation theorem for probability measures in terms of generalized Riesz products. The latter result invo...

A Family of Generalized Riesz Products

Generalized Riesz products similar to the type which arise as the spectral measure for a rank-one transformation are studied. A condition for the mutual singularity of two such measures is given. As an application, a probability space of transformations is presented in which almost all transformations are singular with respect to Lebesgue measure. AMS Subject Classification: Primary 28D03; Seco...

GENERALIZED RIESZ PRODUCTS ON THE BOHR COMPACTIFICATION OF Rp ̊q

We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on R. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of R. Moreover, we discuss the problem of the flat polynomials in this setting. Dedicated to Professors Jean-Paul Thouvenot and Bernard Host. AMS S...

Sidon sets and Riesz products

© Annales de l’institut Fourier, 1985, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...

Generalized Covering Groups and Direct Limits