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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2024, Volume 517, Pages 85–91
DOI: https://doi.org/10.31857/S2686954324030144 (Mi danma535) 		 
MATHEMATICS

Representations of solutions for Volterra integro-differential equations in Hilbert spaces

N. A. Rautianab

a Lomonosov Moscow State University, Moscow, Russian Federation
b Moscow Center for Fundamental and Applied Mathematics, Moscow, Russian Federation
DOI: https://doi.org/10.31857/S2686954324030144
Abstract: Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.
Keywords: Volterra integro-differential equations, linear differential equations in Hilbert spaces, representations of solutions.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15-2022-284
This work was supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under agreement no. 075-15-2022-284.
Presented: V. A. Sadovnichii
Received: 16.04.2024
Revised: 19.05.2024
Accepted: 28.05.2024
English version:
Doklady Mathematics, 2024, Volume 109, Issue 3, Pages 262–267
DOI: https://doi.org/10.1134/S1064562424601240
Bibliographic databases:
Document Type: Article
UDC: 517.968.72
Language: Russian
Citation: N. A. Rautian, “Representations of solutions for Volterra integro-differential equations in Hilbert spaces”, Dokl. RAN. Math. Inf. Proc. Upr., 517 (2024), 85–91; Dokl. Math., 109:3 (2024), 262–267
Citation in format AMSBIB
\Bibitem{Rau24}
\by N.~A.~Rautian
\paper Representations of solutions for Volterra integro-differential equations in Hilbert spaces
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2024
\vol 517
\pages 85--91
\mathnet{http://mi.mathnet.ru/danma535}
\crossref{https://doi.org/10.31857/S2686954324030144}
\elib{https://elibrary.ru/item.asp?id=69204694}
\transl
\jour Dokl. Math.
\yr 2024
\vol 109
\issue 3
\pages 262--267
\crossref{https://doi.org/10.1134/S1064562424601240}
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