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Lobachevskii Journal of Mathematics, 2005, Volume 20, Pages 47–57 (Mi ljm54)  
Generalized solutions of Volterra integral equations of the first kind

M. V. Falaleeva, N. A. Sidorova, D. N. Sidorovb

a Institute of Mathematics, Economics and Informatics of Irkutsk State University
b L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences
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Abstract: In this paper we derived the explicit structure of generalized solutions of the Volterra integral equations of the first kind. The solution contains singular and regular components. These components can be constructed separately. On the first stage we construct the singular component of the solution by solving the special linear algebraic system. On the second stage the regular component of generalized solution can be constructed.
Keywords: Volterra integral equations, Dirac function, resolvent, singular component.
Submitted by: A. M. Elizarov
Received: 29.10.2005
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Language: English
Citation: M. V. Falaleev, N. A. Sidorov, D. N. Sidorov, “Generalized solutions of Volterra integral equations of the first kind”, Lobachevskii J. Math., 20 (2005), 47–57
Citation in format AMSBIB
\Bibitem{FalSidSid05}
\by M.~V.~Falaleev, N.~A.~Sidorov, D.~N.~Sidorov
\paper Generalized solutions of Volterra integral equations of the first kind
\jour Lobachevskii J. Math.
\yr 2005
\vol 20
\pages 47--57
\mathnet{http://mi.mathnet.ru/ljm54}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2193552}
\zmath{https://zbmath.org/?q=an:1113.45002}
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