Vector-valued cosine transforms
In the first part of the paper, vector-valued cosine and sine transforms on a Banach space and the associated functional calculi are introduced. Next, using the cosine transforms, the author gives different, equivalent assertions to characterize the cosine functions. As application, a result of \textit{V.\,Keyantuo} and \textit{P.\,Vieten} [Stud.\ Math.\ 129, No.\,2, 137--156 (1998; Zbl 0910.47035)] is proved with the new approach. Corresponding results for sine functions are also provided.
scientific article; zbMATH DE number 5014175