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}
}
  • F. Bayart, I. Ruzsa
  • 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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87 Citations

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