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 to n-times integrated semigroups and cosine functions, yielding some new results about their approximation. as well as the convergence of their Cesaro and Abel means to the identity. (C) 1997 Academic Press.
