Growth of entire functions: from frequent hypercyclicity to hypercyclicity for the differentiation operator

TL;DR

This paper investigates the growth rates of entire functions that are hypercyclic and frequently hypercyclic under the differentiation operator, establishing optimal bounds and linking their growth behaviors.

Contribution

It introduces new results connecting the minimal growth of frequently hypercyclic functions to hypercyclic functions, with optimal bounds for the differentiation operator.

Findings

Established optimal growth bounds for frequently hypercyclic entire functions.

Linked growth rates of hypercyclic and frequently hypercyclic functions.

Provided new insights into the growth behavior under differentiation operator.

Abstract

We study the rate of growth of entire functions that are frequently hypercyclic with respect to some upper weighted densities for the differentiation operator. The statements obtained show the link between the minimal growth of frequently hypercyclic entire functions and that of hypercyclic entire functions. The results are optimal.