Optimal and Non-optimal Rates of Approximation for Integrated Semigroups and Cosine Functions Original Research Article

For a general approximation process we formulate theorems concerning rates of convergence, including theorems about saturation class, non-optimal rates, and sharpness of non-optimal convergence. The general results are then applied ton-times integrated semigroups and cosine functions, yielding some new results about their approximation, as well as the convergence of their Cesáro and Abel means to the identity.