Asymptotic expansions for Yosida approximations of semigroups

Abstract

In this paper we provide asymptotic expansions for Yosida approximations of contraction semigroups. We also obtain optimal bounds for convergencerate and remainder terms of asymptotic expansions. We use a method introduced in [2] for analysis of errors in Central Limit Theorem and in approximations by accompanying laws. This method was applied in [3] to obtain optimal convergence rates in some approximation formulas for operators and in [10] to obtain asymtotic expansions and optimal error bounds for Euler’s approximations of semigroups.

Keywords

• semigroups
• Yosida approximations
• asymptotic expansions
• holomorphic semigroups
• convergence rate