# Difference sets and frequently hypercyclic weighted shifts

@article{Bayart2013DifferenceSA,
title={Difference sets and frequently hypercyclic weighted shifts},
author={F. Bayart and Imre Z. Ruzsa},
journal={Ergodic Theory and Dynamical Systems},
year={2013},
volume={35},
pages={691 - 709}
}
• Published 10 May 2013
• Mathematics
• Ergodic Theory and Dynamical Systems
Abstract We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on ${\ell }^{p} ( \mathbb{Z} )$, $p\geq 1$. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is $\mathcal{U}$-frequently hypercyclic but not frequently hypercyclic, and that there exists an operator which is frequently hypercyclic but not distributionally chaotic…
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