Abstract Volterra integral equations of wave type with almost sectorial operators

Abstract

We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for the latter type of operators to construct a general class of bounded linear operators that in particular contains the propagators (solution operators) of the considered equations. Some properties of this family of operators are also given.