Chaotic and frequently hypercyclic operators in the weighted space of entire functions

Abstract

We study the issues of chaoticity and frequently hypercyclicity of various operators in the weighted space Fφ(Cn), defined as the projective limit of Banach spaces. Theorems 8–13 consider the cases of differentiation and shift operators, as well as their compositions in Fφ(Cn). For linear continuous operators commuting with differentiation, Theorem 14 shows that they are chaotic in Fφ(Cn). In Theorem 15, such operators are proved to be frequently hypercyclic in Fφ(Cn), and also are the most important consequences of these statements are indicated.