Hermitian and Positive Integrated C-cosine Functions on Banach Spaces

Peculiar properties of hermitian and positive n-times integrated C-cosine functions on Banach spaces are investigated. Among them are: (1) Any nondegenerate positiven -times integrated C-cosine function is infinitely differentiable in operator norm; (2) An exponentially bounded, nondegenerateC -cosine function on Lp(μ) (1<p<∞) (orL1(μ), C0 , in case C has dense range) is positive if and only if its generator is bounded, positive, and commutes with C.