On the convergence of rational approximations of semigroups on intermediate spaces

摘要

We generalize a result by Brenner and Thomee on the rate of convergence of rational approximation schemes for semigroups. Using abstract interpolation techniques we obtain convergence on a continuum of intermediate spaces between the Banach space X and the domain of a certain power of the generator of the semigroup. The sharpness of the results is also discussed.