# 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} }

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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