Frequently hypercyclic semigroups

Volume 202 / 2011

Elisabetta M. Mangino, Alfredo Peris Studia Mathematica 202 (2011), 227-242 MSC: Primary 47A16; Secondary 47D06. DOI: 10.4064/sm202-3-2

Abstract

We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis integral. This criterion can be verified in certain cases in terms of the infinitesimal generator of the semigroup. Applications are given for semigroups generated by Ornstein–Uhlenbeck operators, and especially for translation semigroups on weighted spaces of $p$-integrable functions, or continuous functions that, multiplied by the weight, vanish at infinity.

Authors

  • Elisabetta M. ManginoDipartimento di Matematica “Ennio De Giorgi”
    Università del Salento
    I-73100 Lecce, Italy
    e-mail
  • Alfredo PerisIUMPA
    Universitat Politècnica de València
    Departament de Matemàtica Aplicada
    Edifici 7A
    E-46022 Valéncia, Spain
    e-mail

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