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Rate of growth of frequently hypercyclic functions

Part of: General theory of linear operators Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  12 January 2010

O. Blasco ,
A. Bonilla  and
K.-G. Grosse-Erdmann
O. Blasco
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, 46100 Burjassot, Valencia, Spain, Email: (oscar.blasco@uv.es)
A. Bonilla
Affiliation:
Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna (Tenerife), Spain, Email: (abonilla@ull.es)
K.-G. Grosse-Erdmann
Affiliation:
Institut de Mathématique, Université de Mons, 7000 Mons, Belgium, Email: (kg.grosse-erdmann@umons.ac.be)
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Abstract

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We study the rate of growth of entire functions that are frequently hypercyclic for the differentiation operator or the translation operator. Moreover, we prove the existence of frequently hypercyclic harmonic functions for the translation operator and we study the rate of growth of harmonic functions that are frequently hypercyclic for partial differentiation operators.

Keywords

frequently hypercyclic operatorfrequently hypercyclic vectorFrequent Hypercyclicity Criterionrate of growthentire functionharmonic function

MSC classification

Secondary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 30D15: Special classes of entire functions and growth estimates
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 39 - 59
Copyright
Copyright © Edinburgh Mathematical Society 2010