Hermite expansions of C0C0-groups and cosine functions

In this paper we introduce vector-valued Hermite expansions to approximate one-parameter operator families such as C0C0-groups and cosine functions. In both cases we estimate the rate of convergence of these Hermite expansions to the related family and compare to other already known approximations. Finally, we illustrate our results with particular examples of C0C0-groups and cosine functions and their Hermite expansions.