Representations of the solutions for volterra integro-differential equations in hilbert spaces

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Abstract

Volterra integro-differential equations with operator coefficients in Hilbert spaces were studied. The relationship has been established between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of semigroups. Representations of solutions for considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator-functions.

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About the authors

N. A. Rautian

Lomonosov Moscow State University; Moscow Center for Fundamental and Applied Mathematics

Author for correspondence.
Email: nadezhda.rautian@math.msu.ru
Russian Federation, Moscow; Moscow

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