On aperiodicity and hypercyclic weighted translation operators. (English) Zbl 1481.47007
Summary: We find several equivalent characterizations of aperiodicity of an element on a locally compact group \(G\), and give an intuition for “how strong the aperiodicity of an element affects the existence of hypercyclic weighted translation operators.” In fact, if \(a\) is an aperiodic element in \(G\), then there exists a mixing, chaotic and frequently hypercyclic weighted translation \(T_{a, w}\) on \(L^p(G)\).
MSC:
| 47A16 | Cyclic vectors, hypercyclic and chaotic operators |
| 22D05 | General properties and structure of locally compact groups |
Keywords:
aperiodicity; chaos; frequent hypercyclicity; hypercyclicity; weighted translation operator; locally compact groupReferences:
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