Approximation of Integrated Semigroups by 'Integrated' Discrete Parameter Semigroups

摘要

In this paper we study the problem of approximation of a locally Lipschitz continuous integrated semigroup on a Banach space X with norm || . || by a sequence of "integrated" discrete parameter semigroups 0 Tn ds : t > 0 on Xn, where {hn} is a positive null sequence and Tn is a bounded linear operator on a Banach space Xn with norm || . ||n. Here {Xn} is a sequence of Banach spaces approximating X in the following sense: There exist bounded linear operators Pn on X to Xn such that.