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# Recurrence of Cosine Operator Functions on Groups

Published:2016-03-18
Printed: Dec 2016
• Chung-Chuan Chen,
Department of Mathematics Education, National Taichung University of Education, Taiwan
 Format: LaTeX MathJax PDF

## Abstract

In this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.
 Keywords: topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function
 MSC Classifications: 47A16 - Cyclic vectors, hypercyclic and chaotic operators 54B20 - Hyperspaces 43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.

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