Frequently hypercyclic sequences of differential operators on the space of entire functions

TL;DR

This paper establishes a criterion for frequent hypercyclicity of sequences of convolution operators on entire functions, based on the non-vanishing of generating functions and control of their modulus.

Contribution

It introduces a new criterion for frequent hypercyclicity of differential operator sequences on entire functions, linking spectral properties to hypercyclic behavior.

Findings

Provides a criterion involving non-vanishing generating functions on an annulus.

Links the modulus control of sequence terms to hypercyclicity.

Applies to sequences of convolution operators on entire functions.

Abstract

A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on an appropriate annulus, in the boundary of which the modulus of each term of the sequence is in some sense controlled by the preceding ones or the following ones.