Frequently hypercyclic semigroups

Elisabetta M. Mangino; Alfredo Peris

Studia Mathematica (2011)

  • Volume: 202, Issue: 3, page 227-242
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Elisabetta M. Mangino, and Alfredo Peris. "Frequently hypercyclic semigroups." Studia Mathematica 202.3 (2011): 227-242. <http://eudml.org/doc/285445>.

@article{ElisabettaM2011,
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.},
author = {Elisabetta M. Mangino, Alfredo Peris},
journal = {Studia Mathematica},
keywords = {chaotic -semigroups; frequently hypercyclic -semigroups; translation semigroups},
language = {eng},
number = {3},
pages = {227-242},
title = {Frequently hypercyclic semigroups},
url = {http://eudml.org/doc/285445},
volume = {202},
year = {2011},
}

TY - JOUR
AU - Elisabetta M. Mangino
AU - Alfredo Peris
TI - Frequently hypercyclic semigroups
JO - Studia Mathematica
PY - 2011
VL - 202
IS - 3
SP - 227
EP - 242
AB - 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.
LA - eng
KW - chaotic -semigroups; frequently hypercyclic -semigroups; translation semigroups
UR - http://eudml.org/doc/285445
ER -

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