Complex Analysis and Operator Theory

, Volume 7, Issue 1, pp 33–42 | Cite as

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.

Keywords

Weighted spaces of entire functions Differentiation operator Hypercyclic operator Chaotic operator Frequently hypercyclic operator 

Mathematics Subject Classification (2000)

Primary 47A16 Secondary 46E15 47B38 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática, Pura y Aplicada IUMPAUniversidad Politécnica de ValenciaValenciaSpain
  2. 2.Departamento de Análisis MatemáticoUniversidad de La LagunaLa Laguna (Tenerife)Spain

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