Evolution operator

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