Disjoint hypercyclicity of weighted translations

TL;DR

This paper investigates conditions under which multiple weighted translation operators on $L^p(G)$ exhibit disjoint hypercyclicity, contributing to the understanding of operator dynamics on function spaces.

Contribution

It provides a sufficient condition for disjoint hypercyclicity of finitely many weighted translations on $L^p(G)$, advancing the theory of operator hypercyclicity.

Findings

Established a sufficient condition for disjoint hypercyclicity

Extended hypercyclicity theory to weighted translations on $L^p(G)$

Contributed to the understanding of operator dynamics on locally compact groups

Abstract

Given a locally compact group $G$ and $1\leq p<\infty$, a sufficient condition ensuring the \emph{disjoint hypercyclicity} of finitely many weighted translations on $L^p(G)$ was investigated in this paper.