RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Sibirsk. Mat. Zh.: Year: Volume: Issue: Page: Find

 Sibirsk. Mat. Zh., 2017, Volume 58, Number 5, Pages 1091–1097 (Mi smj2921)

On systems of linear functional equations of the second kind in $L_2$

V. B. Korotkov

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We consider a general system of functional equations of the second kind in $L_2$ with a continuous linear operator $T$ satisfying the condition that zero lies in the limit spectrum of the adjoint operator $T^*$. We show that this condition holds for the operators of a wide class containing, in particular, all integral operators. The system under study is reduced by means of a unitary transformation to an equivalent system of linear integral equations of the second kind in$L_2$ with Carleman matrix kernel of a special kind. By a linear continuous invertible change, this system is reduced to an equivalent integral equation of the second kind in $L_2$ with quasidegenerate Carleman kernel. It is possible to apply various approximate methods of solution for such an equation.

Keywords: system of linear functional equations of the second kind, integral operator, Carleman integral operator, Hilbert–Schmidt operator, Fredholm resolvent, resolvent kernel, spectrum, limit spectrum.

DOI: https://doi.org/10.17377/smzh.2017.58.511

Full text: PDF file (267 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:5, 845–849

Bibliographic databases:

Document Type: Article
UDC: 517.983+517.968.25
MSC: 35R30

Citation: V. B. Korotkov, “On systems of linear functional equations of the second kind in $L_2$”, Sibirsk. Mat. Zh., 58:5 (2017), 1091–1097; Siberian Math. J., 58:5 (2017), 845–849

Citation in format AMSBIB
\Bibitem{Kor17} \by V.~B.~Korotkov \paper On systems of linear functional equations of the second kind in~$L_2$ \jour Sibirsk. Mat. Zh. \yr 2017 \vol 58 \issue 5 \pages 1091--1097 \mathnet{http://mi.mathnet.ru/smj2921} \crossref{https://doi.org/10.17377/smzh.2017.58.511} \elib{http://elibrary.ru/item.asp?id=29947474} \transl \jour Siberian Math. J. \yr 2017 \vol 58 \issue 5 \pages 845--849 \crossref{https://doi.org/10.1134/S0037446617050111} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000413438200011} \elib{http://elibrary.ru/item.asp?id=31125406} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85032002394}