Geodesic
Frequently hypercyclic semigroups
Elisabetta M. Mangino 1   ; Alfredo Peris 2
1 Dipartimento di Matematica “Ennio De Giorgi” Università del Salento I-73100 Lecce, Italy
2 IUMPA Universitat Politècnica de València Departament de Matemàtica Aplicada Edifici 7A E-46022 Valéncia, Spain
Studia Mathematica, Tome 202 (2011) no. 3, pp. 227-242 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm202-3-2
Keywords: study frequent hypercyclicity context strongly continuous semigroups operators precisely criterion sufficient condition semigroup frequently hypercyclic whose formulation depends pettis integral criterion verified certain cases terms infinitesimal generator semigroup applications given semigroups generated ornstein uhlenbeck operators especially translation semigroups weighted spaces p integrable functions continuous functions multiplied weight vanish infinity

Elisabetta M. Mangino  1   ; Alfredo Peris  2

1 Dipartimento di Matematica “Ennio De Giorgi” Università del Salento I-73100 Lecce, Italy
2 IUMPA Universitat Politècnica de València Departament de Matemàtica Aplicada Edifici 7A E-46022 Valéncia, Spain 
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Elisabetta M. Mangino; Alfredo Peris. Frequently hypercyclic semigroups. Studia Mathematica, Tome 202 (2011) no. 3, pp. 227-242. doi: 10.4064/sm202-3-2

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