Chaos in convolution operators on the space of entire functions of infinitely many complex variables

Abstract

A classical result of Godefroy and Shapiro states that every nontrivial convolution operator on the space H(C n ) of entire functions of several complex variables is hypercyclic. In sharp contrast with this result Fávaro and Mujica show that no translation operator on the space H(C N ) of entire functions of infinitely many complex variables is hypercyclic. In this work we study the linear dynamics of convolution operators on H(C N ). First we show that no convolution operator on H(C N ) is neither cyclic nor n-supercyclic for any positive integer n. After we study the notion of Li-Yorke chaos in non-metrizable topological vector spaces and we show that every nontrivial convolution operator on H(C N ) is Li-Yorke chaotic.