Classical operators on the Hörmander algebras

María José Beltrán; José Bonet; Carmen Fernández

doi:10.3934/dcds.2015.35.637

Article Contents

2015, Volume 35, Issue 2: 637-652. Doi: 10.3934/dcds.2015.35.637

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Classical operators on the Hörmander algebras

1.
Facultad de Magisterio, Universitat de València, Avda. Tarongers, 4, E-46022-Valencia
2.
Instituto Universitario de Matemática Pura y Aplicada, IUMPA Universitat Politència, Camino de Vera, s/n., E-46022 Valencia
3.
Departamento de Análisis Matemático, Universitat de València, C/ Dr. Moliner, 50, E-46100-Burjassot

Received: June 30, 2013

Revised: September 30, 2013

Published: January 2015

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Abstract

We study the integration operator, the differentiation operator and more general differential operators on radial Fréchet or (LB) Hörmander algebras of entire functions. We analyze when these operators are power bounded, hypercyclic and (uniformly) mean ergodic.

Keywords:

Hypercyclic,
chaotic,
power bounded and (uniformly) mean ergodic operators,
differential operators,
entire functions,
growth conditions,
weighted spaces of entire functions,
Hörmander algebras.

Mathematics Subject Classification: Primary: 47B38; Secondary: 47A16, 46E15.

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