, Volume 7, Issue 1, pp 33-42
Date: 11 Feb 2011

Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions

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Abstract

Motivated by recent work on the rate of growth of frequently hypercyclic entire functions due to Blasco, Grosse-Erdmann and Bonilla, we investigate conditions to ensure that the differentiation operator is chaotic or frequently hypercyclic on generalized weighted Bergman spaces of entire functions studied by Lusky, whenever the differentiation operator is continuous. As a consequence we partially complete the knowledge of possible rates of growth of frequently hypercyclic entire functions for the differentiation operator.

Communicated by Daniel Aron Alpay.
J. Bonet is partially supported by MICINN and FEDER Projects MTM 2007-62643 and MTM2010-15200, GV Project Prometeo/2008/101 and UPV Project 2773.
A. Bonilla is supported by MICINN and FEDER Project MTM2008-05891.