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Evolution operator

From Encyclopedia of Mathematics
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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
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article