Rates of approximation and ergodic limits of regularized operator families

Abstract

We state mean ergodic theorems with rates of approximation for a new class of operator families. Our result provides a unified approach to convergence rates for many particular strongly continuous solution families associated to linear evolution equations such as the abstract Cauchy problem of the first and second order, and integral Volterra equations of convolution type. We discuss in particular, applications to α-times integrated cosine families, k-convoluted semigroups and integral resolvents.