Correct solvability of integrodifferential equations in spaces of vector functions holomorphic in an angular domain

Integrodifferential equations with unbounded operator coefficients in a Hilbert space are studied. The main part of an equation of this kind is an abstract parabolic equation perturbed by a Volterra integral operator. The fundamental difference between this work and the other ones is that integrodifferential equations are considered and studied in this paper for vector functions the arguments of which take values in an angular domain on the complex plane.