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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: 26.10.2011

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
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\paper Systems of convolution equations of the first and second kind on a~finite interval and factorization of matrix-functions
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\pages 978--990
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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  mathnet  crossref
    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  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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