Evolution operator
From Encyclopedia of Mathematics
A linear operator-function of two variables t and s that satisfies the properties 1) U(s,s) = I; 2) U(t,x)U(x,s) = U(t,s); and 3) U(t,s) = U(s,t)^{-1}.
Comments
In general, an evolution operator can be defined as a (not necessarily linear) operator-function U(t,s) satisfying 1) and 2). If t,s are not subjected to restrictions, 3) is satisfied automatically. Under some circumstances, the restriction t \ge s is a natural one, and the inverse need not exist at all.
References
[a1] | A. Pazy, "Semigroups of linear operators and applications to partial differential equations" , Springer (1983) pp. Chapt. 5 |
How to Cite This Entry:
Evolution operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Evolution_operator&oldid=42088
Evolution operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Evolution_operator&oldid=42088
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article