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

100%

Grivaux S.

Studia Mathematica

2013

tom 215

nr 3

237-259

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.

A probabilistic version of the Frequent Hypercyclicity Criterion

100%

Grivaux S.

Studia Mathematica

2006

tom 176

nr 3

279-290

For a bounded operator T on a separable infinite-dimensional Banach space X, we give a "random" criterion not involving ergodic theory which implies that T is frequently hypercyclic: there exists a vector x such that for every non-empty open subset U of X, the set of integers n such that Tⁿx belongs to U, has positive lower density. This gives a connection between two different methods for obtaining the frequent hypercyclicity of operators.

Ograniczanie wyników

2 Studia Mathematica

2 Grivaux S.

1 2013

1 2006

Wyniki wyszukiwania

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

A probabilistic version of the Frequent Hypercyclicity Criterion