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

• Autorzy: Sophie Grivaux
• Języki publikacji: EN

Abstrakty

EN

If $(n_{k})_{k≥1}$ is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle 𝕋 is said to be IP-Dirichlet with respect to $(n_{k})_{k≥1}$ if $σ̂(∑_{k∈ F}n_{k}) → 1$ as F runs over all non-empty finite subsets F of 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.

Kategorie tematyczne

• 42A55: Lacunary series of trigonometric and other functions; Riesz products
• 37A25: Ergodicity, mixing, rates of mixing
• 37A45: Relations with number theory and harmonic analysis
• 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 215
• Numer: 3
• Strony: 237-259

Daty

wydano

2013

Twórcy

autor

Sophie Grivaux

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

Identyfikatory

DOI

10.4064/sm215-3-3