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

We study the issues of chaoticity and frequently hypercyclicity of various operators in the weighted space F φ (C n ), 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 F φ (C n ). For linear continuous operators commuting with differentiation, Theorem 14 shows that they are chaotic in F φ (C n ). In Theorem 15, such operators are proved to be frequently hypercyclic in F φ (C n ), and also are the most important consequences of these statements are indicated.