Multiplicative structures of hypercyclic functions for convolution operators

TL;DR

This paper demonstrates the existence of an infinitely generated multiplicative group of entire functions that are hypercyclic under convolution operators, and explores stability of hypercyclicity under multiplication and composition.

Contribution

It establishes the existence of a large algebraic structure of hypercyclic functions for convolution operators and analyzes stability properties under multiplication and composition.

Findings

Existence of an infinitely generated multiplicative group of hypercyclic functions.

Hypercyclicity is stable under multiplication for certain functions.

Stability of compositional hypercyclicity on complex domains.

Abstract

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.