# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Frequently hypercyclic semigroups

### Tom 202 / 2011

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

#### Streszczenie

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.

#### Autorzy

• Elisabetta M. ManginoDipartimento di Matematica “Ennio De Giorgi”
Università del Salento
I-73100 Lecce, Italy
e-mail
• Alfredo PerisIUMPA
Universitat Politècnica de València