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Abstract and Applied Analysis
Volume 2014, Article ID 603234, 7 pages
http://dx.doi.org/10.1155/2014/603234
Research Article

Chaos for Cosine Operator Functions on Groups

Department of Mathematics Education, National Taichung University of Education, Taichung 403, Taiwan

Received 18 December 2013; Revised 11 February 2014; Accepted 11 February 2014; Published 13 March 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Chung-Chuan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let and be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space , in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.