Hypercyclicity, existence and approximation results for convolution operators on spaces of entire functions

TL;DR

This paper develops a general framework for analyzing convolution operators on spaces of entire functions, establishing new hypercyclicity, existence, and approximation results, with applications to functions on complex n-dimensional spaces.

Contribution

It introduces a unified method to derive hypercyclicity and approximation results for convolution operators on entire functions, extending previous literature and applying to higher-dimensional complex spaces.

Findings

New hypercyclicity results for convolution operators on entire functions.

Existence and approximation theorems for convolution equations.

Applications to entire functions on ^n with novel results.

Abstract

In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and existence and approximation results for convolution equations on spaces of entire functions of a given type and order. In both cases we give a general method to prove new results that recover, as particular cases, several results of the literature. Applications of these more general results are given, including new hypercyclicity results for convolution operators on spaces on entire functions on $\mathbb{C}^n.$