# Journal of Operator Theory

Volume 80, Issue 1,  Summer  2018  pp. 213-224.

Multiplicative structures of hypercyclic functions for convolution operators

Authors:  Luis Bernal-Gonzalez (1), J. Alberto Conejero (2), George Costakis (3), and Juan B. Seoane-Sepulveda (4)
Author institution: (1) Departamento de Analisis Matematico, Facultad de Matematicas, Universidad de Sevilla, Avenida Reina Mercedes, 41080 Sevilla, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, 46022 Valencia, Spain
(3) Department of Mathematics and Applied Mathematics, University of Crete, Voutes Campus, 70013 Heraklion, Crete, Greece
Summary:  In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function $1$, hypercyclic with respect to the convolution operator associated to a given entire function of subexponential type. A certain stability under multiplication is also shown for compositional hypercyclicity on complex domains.