局部緊緻群上的權重平移算子

Abstract

我們主要探討的問題是「局部緊緻群上是否存在超循環權重平移算子？」。首先我們刻劃了非週期性元素的一些等價條件，並給出非週期性元素的超循環權重平移算子存在性。另一方面，我們也給出一些週期性元素的權重平移算子是超循環算子的必要條件。

Our main question is ``Does there exist a hypercyclic weighted translation operator on locally compact groups?'. In this article, we give several equivalent characterization of aperiodicity of an element on locally compact group. If a is an aperiodic element, we show that there exists a frequently hypercyclic weighted translation T_{a,w}. If a is a periodic element, we give necessary conditions of hypercyclic weighted translation T_{a,w}.