ИСТИНА

We study integro-differential equations with unbounded operator coefficients in Hilbert spaces. The principal part of the equation is an abstract hyperbolic equation perturbed by summands with Volterra integral operators. These equations represent an abstract form of the integro-partial differential equation arising in viscoelasticity theory, heat conduction theory in media with memory, etc. A spectral analysis of the operator-valued functions, which are the symbols of considered integro-differential equations is provided.