Chaos for Cosine Operator Functions on Groups

Abstract EN

Let 1 ≤ p < ∞ 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.