Hypercyclic behavior of some non-convolution operators on $H({\mathbb{C}}^N)$

Abstract

We study hypercyclicity properties of a family of non-convolution operators defined on spaces of holomorphic functions on ${\mathbb{C}}^N$. 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 $H(\mathbb{C})$. The hypercyclic behavior is more involved than in the one dimensional case, and depends on several parameters involved.

References in corpus (1)

• Strong mixing measures for linear operators and frequent hypercyclicity