Hypercyclic behavior of some non-convolution operators on H(CN)

Abstract

We study hypercyclicity properties of a family of non-convolution operators defined on the spaces of entire functions on CN. These operators are a composition of a differentiation operator and an affine composition operator, and are analogues of operators studied by Aron and Markose on H(C). The hypercyclic behavior is more involved than in the one dimensional case, and depends on several parameters involved.