q-Frequently hypercyclic operators

Abstract

We introduce q-frequently hypercyclic operators and derive a sufficient criterion for a continuous operator to be q-frequently hypercyclic on a locally convex space. Applications are given to obtain q-frequently hypercyclic operators with respect to the norm-, F-norm- and weak*- topologies. Finally, the frequent hypercyclicity of the non-convolution operator $T_{\mu }$ defined by $T_{\mu }(f)(z)=f^{\prime }(\mu z)$, $\mu \ge 1$ on the space $H(\mathbb{C})$ of entire functions equipped with the compact-open topology is shown.

13 pages, to appear