Spectral Analysis of the Generators for Semigroups Associated with Volterra Integro-Differential Equations

Abstract The paper studies the properties of a linear operator that is the generator of a semigroup associated with Volterra integro-differential equations in Hilbert spaces. These integro-differential equations can be realized as partial integro-differential equations arising in the theory of viscoelasticity and the theory of heat propagation in media with memory and have a number of other important applications. The results obtained in the paper can be used to study the behavior of and obtain estimates for the solutions of Volterra integro-differential equations.

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