Mangino, Elisabetta M.; Peris, Alfredo Frequently hypercyclic semigroups. (English) Zbl 1232.47007 Stud. Math. 202, No. 3, 227-242 (2011). If \(X\) is a separable infinite-dimensional Banach space, a \(C_{0}\)-semigroup \((T_{t})_{t\geq 0}\) of bounded linear operators on \(X\) is said to be hypercyclic if there exists a vector \(x\in X\) such that \(\{T_{t} x \mid t\geq 0\}\) is dense in \(X\), and frequently hypercyclic if there exists a vector \(x\in X\) such that for any non-empty open subset \(U\) of \(X\), the set \(\{t\geq 0 \mid T_{t}x\in U\}\) has positive lower density. In this paper, the authors prove a version for \(C_{0}\)-semigroups of the so-called Frequent Hypercyclicity Criterion. Applications are given to semigroups generated by Ornstein-Uhlenbeck operators, in particular to translation semigroups on weighted spaces of \(L^{p}\)-functions or continuous functions which, when multiplied by the weight, vanish at infinity. Reviewer: Sophie Grivaux (Villeneuve d’Ascq) Cited in 1 ReviewCited in 22 Documents MSC: 47A16 Cyclic vectors, hypercyclic and chaotic operators 47D06 One-parameter semigroups and linear evolution equations Keywords:chaotic \(C_0\)-semigroups; frequently hypercyclic \(C_0\)-semigroups; translation semigroups PDFBibTeX XMLCite \textit{E. M. Mangino} and \textit{A. Peris}, Stud. Math. 202, No. 3, 227--242 (2011; Zbl 1232.47007) Full Text: DOI arXiv Link