Hypercyclic Algebras for convolution operators of unimodular constant term

Abstract

We study the existence of hypercyclic algebras for convolution operators $\hat{I}¦(D)$ on the space of entire functions whose symbol $\hat{I}¦$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of densely strongly algebrable sets of hypercyclic vectors.