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Mediterranean Journal of Mathematics

, Volume 7, Issue 1, pp 101–109 | Cite as

Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators

  • José A. Conejero
  • Elisabetta M. Mangino
Article

Abstract

The chaotic and hypercyclic behavior of the C 0-semigroups of operators generated by a perturbation of the Ornstein-Uhlenbeck operator with a multiple of the identity in \({L^2(\mathbb {R}^N)}\) is investigated. Negative and positive results are presented, depending on the signs of the real parts of the eigenvalues of the matrix appearing in the drift of the operator.

Mathematics Subject Classification (2010)

Primary 47A16 Secondary 47D06 47D07 

Keywords

Ornstein-Uhlenbeck operator chaotic C0-semigroups hypercyclic C0-semigroup 

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Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y AplicadaUniversidad Politécnica de ValenciaValenciaSpain
  2. 2.Dipartimento di Matematica “E. De Giorgi”Università del SalentoLecceItaly

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