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 Sibirsk. Mat. Zh., 2013, Volume 54, Number 6, Pages 1294–1303 (Mi smj2496)

Linear functional equations of the first, second, and third kind in $L_2$

V. B. Korotkov

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

Abstract: Under consideration are the functional equations of the first, second, and third kind with operators in wide classes of linear continuous operators in $L_2$ containing all integral operators. We propose methods for reducing these equations by linear invertible changes either to linear integral equations of the first kind with nuclear operators or to equivalent linear integral equations of the second kind with quasidegenerate Carleman kernels. Some various approximate methods of solution are applicable to the so-obtained integral equations.

Keywords: linear functional equation of the first, second and third kind in $L_2$, almost compact operator, integral operator, Carleman integral operator, Hilbert–Schmidt operator, nuclear operator, kernel, quasidegenerate kernel, degenerate kernel.

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English version:
Siberian Mathematical Journal, 2013, 54:6, 1029–1036

Bibliographic databases:

UDC: 517.983+517.968.25

Citation: V. B. Korotkov, “Linear functional equations of the first, second, and third kind in $L_2$”, Sibirsk. Mat. Zh., 54:6 (2013), 1294–1303; Siberian Math. J., 54:6 (2013), 1029–1036

Citation in format AMSBIB
\Bibitem{Kor13} \by V.~B.~Korotkov \paper Linear functional equations of the first, second, and third kind in $L_2$ \jour Sibirsk. Mat. Zh. \yr 2013 \vol 54 \issue 6 \pages 1294--1303 \mathnet{http://mi.mathnet.ru/smj2496} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184095} \transl \jour Siberian Math. J. \yr 2013 \vol 54 \issue 6 \pages 1029--1036 \crossref{https://doi.org/10.1134/S0037446613060098} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000329110700009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84891332823} 

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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. V. B. Korotkov, “On systems of linear functional equations of the third kind in $L_2$”, Siberian Math. J., 56:3 (2015), 435–441
2. V. B. Korotkov, “Integral equations of the third kind with unbounded operators”, Siberian Math. J., 58:2 (2017), 255–263
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