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.
"Chaos for Cosine Operator Functions on Groups." Abstr. Appl. Anal. 2014 (SI05) 1 - 7, 2014. https://doi.org/10.1155/2014/603234