Abstract
We study the correct solvability of initial problems for abstract integrodifferential equations with unbounded operator coefficients in a Hilbert space. We do spectral analysis of operator-functions that are symbols of such equations. The equations under consideration are an abstract form of linear integrodifferential equations with partial derivatives arising in viscoelasticity theory and having a number of other important applications. We describe localization and structure of the spectrum of operatorfunctions that are symbols of such equations.
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