Disjoint hypercyclic powers of weighted translations on groups

Czechoslovak Mathematical Journal

Liang Zhang¹ 

关键词: disjoint hypercyclic powers of weighted translations;    aperiodic element;    locally compact group;   

DOI  :  10.21136/CMJ.2017.0204-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  Let $G$ be a locally compact group and let $1 \le p < \infty.$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^p(G)$ in terms of the weights. Sufficient and necessary conditions for disjoint hypercyclic and disjoint supercyclic powers of weighted translations generated by aperiodic elements on groups will be given.

【 授权许可】

Unknown