Evolution operator
From Encyclopedia of Mathematics
A linear operator-function of two variables
and
that satisfies the properties 1)
; 2)
; and 3)
.
Comments
In general, an evolution operator can be defined as a (not necessarily linear) operator-function satisfying 1) and 2). If
are not subjected to restrictions, 3) is satisfied automatically. If
belong to an infinite-dimensional space, the restriction
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=42087
Evolution operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Evolution_operator&oldid=42087
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article