Geodesic
Disjoint hypercyclic powers of weighted translations on groups
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 839-853
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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.
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.
DOI : 10.21136/CMJ.2017.0204-16
Classification : 46E15, 47A16, 47B38
Keywords: disjoint hypercyclic powers of weighted translations; aperiodic element; locally compact group 
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Zhang, Liang; Lu, Hui-Qiang; Fu, Xiao-Mei; Zhou, Ze-Hua. Disjoint hypercyclic powers of weighted translations on groups. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 839-853. doi: 10.21136/CMJ.2017.0204-16

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