Abstract
A Co semi-group of operators T(t) on a Banach space B into itself can be approximated by formulae known as exponential formulae [5, p. 359]. The rate of convergence of some of the exponential formulae in terms of the moduli of continuity of T(t)f and AT(t)f, where A is the infinitesimal generator, was investigated in [1], [3], and [4]. In this paper we shall find the optimal rate of convergence, that is, the saturation sequence, and the class of functions on which it is achieved, that is the saturation class for exponential formulae satisfying certain conditions. These conditions are satisfied by the exponential formulae of Hille, Kendall, Post-Widder and Phillips. Also, it is important to note that the results depend only on points in (t,t+δ) for some δ (no matter how small).
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