Abstract
In this paper we deal with the weighted Banach algebra L 1 (ℝ+, * c ), where *c is the cosine convolution product. We describe its character space and its multiplier algebra. Our main results concern bounded algebra homomorphisms from L 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.
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