International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 1, Pages 31-40

Semigroup structure underlying evoluations

G. Edgar Parker

Department of Mathematics, Pan American University, Edinburg 78539, Texas, USA

Received 4 December 1979

Copyright © 1982 G. Edgar Parker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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(ts)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.