Supercyclic properties of extended eigenoperators of the differentiation operator on the space of entire functions

TL;DR

This paper characterizes when extended eigenoperators of the differentiation operator on entire functions are supercyclic, hypercyclic, or have supercyclic subspaces, advancing understanding of operator dynamics in functional analysis.

Contribution

It provides a complete characterization of supercyclic and hypercyclic properties of extended eigenoperators of the differentiation operator on entire functions.

Findings

Identifies conditions for supercyclicity of extended eigenoperators.

Determines when such operators have hypercyclic subspaces.

Establishes criteria for the existence of supercyclic subspaces.

Abstract

A continuous linear operator L defined on the space of entire functions H(C) is said to be an extended $lambda$-eigenoperator of the differentiation operator D provided DL = $lambda$LD. Here we fully characterize when an extended $lambda$-eigenoperator of D is supercyclic, it has a hypercyclic subspace or it has a supercyclic subspace.