Applications of the Theory of Abstract Inverse Problems to Partial Differential Equations

Assume that the operators ai(x, t), 0 ~ i ~ n, are symmetric and the operator ao(x, t) is positive definite uniformly in the variables x, t. Of great importance is the case when the space H is finite-dimensional. If this happens, equation (9.1.1) admits the form of the symmetric t.hyperbolic

system offirst order partial differential equations for the components of the vector-function u. Quite often, in the development of advanced theory that does not matter that the space H is tinite-dimensional, while in notations operator style is much more convenient than matrix one.