Chaos for Cosine Operator Functions on Groups

Abstract

Let and $G$ be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space $L^p(G)$, 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.