局部紧化Hausdorff空间上加权平移的超环性

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2021-06-13 DOI:10.1080/14689367.2021.1931814

Ya Wang, Ze‐hua Zhou

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引用次数: 1

摘要

设G是具有正正则Borel测度的局部紧致第二可数Hausdorff空间，ω是G上的一个权。本文给出了在两种不同情况下作用于加权空间的超循环加权平移的充要条件。此外，还举例说明了第一种情况下的结果推广了Salas[16]研究的单边加权移位的超循环性特征，第二种情况下结果推广了Chen和Chu在[8]中的工作。此外，我们还刻画了这些加权平移的伴随算子的超循环性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hypercyclicity of weighted translations on locally compact Hausdorff spaces

Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight on G. In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted space in two different cases. Also, some examples are given to illustrate that the results in the first case generalize the characterizations on hypercyclicity for unilateral weighted shifts studied by Salas [16], and the results in the second case generalize Chen and Chu's work in [8]. Furthermore, we give characterizations of hypercyclicity for adjoint operators of these weighted translations.

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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences