Hypercyclic algebras for convolution and composition operators

摘要

We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as cos(D), De(D), or e(D) - aI, where 0 a = 1. In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras. (C) 2018 Elsevier Inc. All rights reserved.