Hypercyclicity of convolution operators on spaces of entire functions

TL;DR

This paper generalizes recent results on hypercyclic convolution operators acting on spaces of entire functions of infinitely many variables, using Nachbin's holomorphy types to broaden the theoretical framework.

Contribution

It introduces a generalized approach to hypercyclicity of convolution operators on complex function spaces via Nachbin's holomorphy types, extending prior specific cases.

Findings

Established hypercyclicity conditions for convolution operators

Extended results to broader classes of entire functions

Provided a unified framework using holomorphy types

Abstract

In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fr\'echet spaces of entire functions of bounded type of infinitely many complex variables.