Abstract

In this paper, we introduce the notions of $f$-frequent hypercyclicity and $F$-hypercyclicity for $C$-distribution semigroups in separable Fréchet spaces. We particularly analyze the classes of $q$-frequently hypercyclic $C$-distribution semigroups ($q\geq 1$) and frequently hypercyclic $C$-distribution semigroups, providing a great number of illustrative examples.

Keywords: $C$-distribution semigroups; integrated $C$-semigroups; $f$-frequent hypercyclicity; $q$-frequent hypercyclicity; Fr\' echet spaces.

MSC: 47A16, 47B37, 47D06

Pages:  81$-$94     

Volume  72 ,  Issue  1 ,  2020