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Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators

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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.

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Authors and Affiliations

  1. Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, E-46022, Valencia, Spain

    José A. Conejero

  2. Dipartimento di Matematica “E. De Giorgi”, Università del Salento, I-73100, Lecce, Italy

    Elisabetta M. Mangino

Authors
  1. José A. Conejero
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  2. Elisabetta M. Mangino
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Correspondence to Elisabetta M. Mangino.

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Conejero, J.A., Mangino, E.M. Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators. Mediterr. J. Math. 7, 101–109 (2010). https://doi.org/10.1007/s00009-010-0030-7

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  • DOI: https://doi.org/10.1007/s00009-010-0030-7

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