Abstract:
Systems of nn 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 2n2n. 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.
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
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\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://mathscinet.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}
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Linking options:
https://www.mathnet.ru/eng/smj2323
https://www.mathnet.ru/eng/smj/v53/i5/p978
This publication is cited in the following 4 articles:
A. F. Voronin, “Truncated Wiener-Hopf equation and matrix function factorization”, Sib. elektron. matem. izv., 17 (2020), 1217–1226
A. F. Voronin, “On $\mathbb R$-linear problem and truncated Wiener–Hopf equation”, Siberian Adv. Math., 30:2 (2020), 143–151
A. F. Voronin, “O svyazi obobschennoi kraevoi zadachi Rimana i usechennogo uravneniya Vinera—Khopfa”, Sib. elektron. matem. izv., 15 (2018), 412–421
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
Citation in format AMSBIB
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