Semigroup structure underlying evoluations
Gary E. Parker · International Journal of Mathematics and Mathematical Sciences · 1982
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.