Algebra homomorphisms from cosine convolution algebras

In this paper we deal with the weighted Banach algebra L-omega(1), *(c)), wher *(c) is the cosine convolution product. We describe its character space and its multiplier algebra. Our main results concern bounded algebra homomorphisms from L-omega(1)(R+, * (c) ). We give a variant of Kisynski's theorem for such homomorphisms and characterize them in terms of integrated cosine functions. A generalized form of the Sova-Da Prato-Giusti theorem about generation of cosine functions is also given.