IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products

Sophie Grivaux¹

¹ CNRS, Laboratoire Paul Painlevé, UMR 8524 Université Lille 1 Cité Scientifique 59655 Villeneuve d'Ascq Cedex, France

Studia Mathematica, Tome 215 (2013) no. 3, pp. 237-259

Résumé

If $(n_{k})_{k\ge 1}$ is a strictly increasing sequence of integers, a continuous probability measure $\sigma $ on the unit circle $\mathbb T$ is said to be IP-Dirichlet with respect to $(n_{k})_{k\ge 1}$ if $\hat{\sigma }(\sum_{k\in F}n_{k})\to 1 $ as $F$ runs over all non-empty finite subsets $F$ of $\mathbb N$ and the minimum of $F$ tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz products.

Détail

DOI : 10.4064/sm215-3-3

Keywords: strictly increasing sequence integers continuous probability measure sigma unit circle mathbb said ip dirichlet respect hat sigma sum runs non empty finite subsets mathbb minimum tends infinity ip dirichlet measures their connections ip rigid dynamical systems have recently investigated aaronson hosseini lema czyk simplify generalize their results using approach involving generalized riesz products