Rate of growth of hypercyclic and frequently hypercyclic functions for the Dunkl operator

TL;DR

This paper determines the critical growth rates of hypercyclic and frequently hypercyclic entire functions under the Dunkl operator, advancing understanding of their behavior in complex analysis.

Contribution

It identifies the precise growth rates of hypercyclic and frequently hypercyclic functions for the Dunkl operator, a novel analysis in this context.

Findings

Critical growth rate for hypercyclic functions established

Growth rate for frequently hypercyclic functions analyzed

Provides new insights into Dunkl operator dynamics

Abstract

For the Dunkl operator $\Lambda_\alpha$ $(\alpha > -1/2)$ on the space of entire functions on the complex space C, the critical rate of growth for the integral means $M_p(f,r)$ of their hypercyclic functions $f$ is obtained. The rate of growth of the corresponding frequently hypercyclic functions is also analyzed.