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

Tom 215 / 2013

Sophie Grivaux Studia Mathematica 215 (2013), 237-259 MSC: 37A25, 42A16, 42A55, 37A45. DOI: 10.4064/sm215-3-3


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.


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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek