Characterizations of almost periodic strongly continuous cosine operator functions
The almost periodic and uniformly almost periodic cosine operator functions are characterized in terms of their infinitesimal generator; the results extend those due to \textit{H. Bart} and \textit{S. Goldberg} [Math. Ann. 236, 105-116 (1978; Zbl 0365.47019)] for the case of semi- groups of class \(c_ 0\). The main result is: A strongly continuous cosine operator function is almost periodic iff it is uniformly bounded and its infinitesimal generator has a total set of eigenvectors.
uniformly almost periodic cosine operator functions
scientific article; zbMATH DE number 3975713