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 Sibirsk. Mat. Zh., 2012, Volume 53, Number 5, Pages 978–990 (Mi smj2323)

Systems of convolution equations of the first and second kind on a finite interval and factorization of matrix-functions

A. F. Voronin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: Systems of $n$ convolution equations of the first and second kind on a finite interval are reduced to a Riemann boundary value problem for a vector function of length $2n$. We prove a theorem about the equivalence of the Riemann problem and the initial system. Sufficient conditions are obtained for the well-posedness of a system of the second kind. Also under study is the case of the periodic kernel of the integral operator of a system of the first and second kind.

Keywords: system of convolution equations, finite interval, factorization, Riemann boundary value problem, partial indices.

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English version:
Siberian Mathematical Journal, 2012, 53:5, 781–791

Bibliographic databases:

UDC: 517.968+517.544

Citation: A. F. Voronin, “Systems of convolution equations of the first and second kind on a finite interval and factorization of matrix-functions”, Sibirsk. Mat. Zh., 53:5 (2012), 978–990; Siberian Math. J., 53:5 (2012), 781–791

Citation in format AMSBIB
\Bibitem{Vor12} \by A.~F.~Voronin \paper Systems of convolution equations of the first and second kind on a~finite interval and factorization of matrix-functions \jour Sibirsk. Mat. Zh. \yr 2012 \vol 53 \issue 5 \pages 978--990 \mathnet{http://mi.mathnet.ru/smj2323} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3057680} \transl \jour Siberian Math. J. \yr 2012 \vol 53 \issue 5 \pages 781--791 \crossref{https://doi.org/10.1134/S0037446612050035} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000310374900003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868152783} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. F. Voronin, “O svyazi obobschennoi kraevoi zadachi Rimana i usechennogo uravneniya Vinera—Khopfa”, Sib. elektron. matem. izv., 15 (2018), 412–421
2. A. F. Voronin, “Obobschennaya kraevaya zadacha Rimana i integralnye uravneniya v svertkakh pervogo i vtorogo roda na konechnom intervale”, Sib. elektron. matem. izv., 15 (2018), 1651–1662
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