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 Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 6, Pages 1332–1390 (Mi izv1716)

A method for constructing a canonical matrix of solutions of a Hilbert problem arising in the solution of convolution equations on a finite interval

B. V. Pal'tsev

Abstract: The Hilbert boundary value problem corresponding to a convolution equation on a finite interval, with kernel belonging to a class singled out earlier by the author, is reduced to a system of integral equations. The solvability of this system in appropriate weighted spaces is studied and an algorithm for constructing a canonical matrix of solutions of the Hilbert problem from certain solutions of the system. Estimates of partial indices are given.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:3, 559–610

Bibliographic databases:

UDC: 517.968.72+53
MSC: Primary 30E25, 45B05, 45E10; Secondary 35Q15, 45E05, 45F05, 44A15, 46E30, 47A53

Citation: B. V. Pal'tsev, “A method for constructing a canonical matrix of solutions of a Hilbert problem arising in the solution of convolution equations on a finite interval”, Izv. Akad. Nauk SSSR Ser. Mat., 45:6 (1981), 1332–1390; Math. USSR-Izv., 19:3 (1982), 559–610

Citation in format AMSBIB
\Bibitem{Pal81} \by B.~V.~Pal'tsev \paper A~method for constructing a~canonical matrix of solutions of a~Hilbert problem arising in the solution of convolution equations on~a~finite interval \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1981 \vol 45 \issue 6 \pages 1332--1390 \mathnet{http://mi.mathnet.ru/izv1716} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=641804} \zmath{https://zbmath.org/?q=an:0501.45004|0491.45006} \transl \jour Math. USSR-Izv. \yr 1982 \vol 19 \issue 3 \pages 559--610 \crossref{https://doi.org/10.1070/IM1982v019n03ABEH001428} 

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Erratum

This publication is cited in the following articles:
1. B. V. Pal'tsev, “Asymptotic behaviour of the spectra of integral convolution operators on a finite interval with homogeneous polar kernels”, Izv. Math., 67:4 (2003), 695–779
2. M. K. Kerimov, “Boris Vasil'evich Pal'tsev (on the occasion of his seventieth birthday)”, Comput. Math. Math. Phys., 50:7 (2010), 1113–1119
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