Hyperbolic Equations of Nonscalar Type

Abstract

The basic properties of Volterra equations of nonscalar type are discussed in this section. Resolvents for such problems are introduced and their relations to wellposedness and variation of parameters formulae are studied. The latter are then used for perturbation results which yield several well-known existence theorems. The generation theorem for the nonscalar case is proved and then applied to the convergence of resolvents and to existence theorems for equations in Hilbert spaces involving operator-valued kernels of positive type.