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.

Highlights

  • Introduction and resultsIn this paper we obtain asymptotic expansions for Yosida approximations of contraction semigroups

  • S (t )x where Sλ(t) is Yosida approximation of semigroup S(t) and coefficiens am do not depend on λ

  • Assume that A is a generator of contraction semigroup and there exists a positive constant K independent of n, λ and t such that conditions (1.3) and (1.4) are satisfied for all λ > 0, t 0 and n = 0, 1, 2

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Summary

Introduction

In this paper we obtain asymptotic expansions for Yosida approximations of contraction semigroups. S (t )x where Sλ(t) is Yosida approximation of semigroup S(t) and coefficiens am do not depend on λ. We obtain optimal bounds for convergence rate S(t)x − Sλ(t)x and remainder terms Dk. To obtain asymptotic expansions we use an approach introduced in [2] for analysis of errors in Central Limit Theorem and in approximations by accompanying laws. In [10] we used this method to obtain asymtotic expansions and optimal error bounds for Euler’s approximations of semigroups.

Results
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