Disjoint frequent hypercyclicity of composition operators

TL;DR

This paper establishes a sufficient condition for two operators to be disjointly frequently hypercyclic, applies it to composition operators on Hardy spaces, and demonstrates examples including weighted shifts.

Contribution

It introduces a new criterion for disjoint frequent hypercyclicity and applies it to composition operators and weighted shifts, simplifying previous results.

Findings

Established a sufficient condition for disjoint frequent hypercyclicity.

Applied the criterion to composition operators on Hardy spaces.

Provided examples of disjointly frequently hypercyclic weighted shifts.

Abstract

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint frequent hypercyclicity of pseudo shifts of a recent paper of Martin et al. and we exhibit two disjointly frequently hypercyclic weighted shifts.