Semigroup structure underlying evoluations

Abstract

A member of a class of evolution systems is defined by averaging a one parameter family of invertible transformations G with a semigroup T. The resulting evolution system, U(t,s)=G(t)T(t−s)G(s)−1, preserves continuity and strong continuity, and in case G is a linear family, may have an identifiable generator and resolvent both of which are constructed from T. Occurrences of the class of evolutions are given to show possible applications.

Keywords

• evolution system
• semigroup of transformations
• resolvent.