Hypercyclic algebras for convolution and composition operators
arXiv:1706.08022
Abstract
We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator 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 $\mbox{cos}(D)$, , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras. Non-trivial translations on the space of complex-valued, smooth functions on the real line do support hypercyclic algebras.
Accepted for publication in J. Funct. Anal