RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Sb.: Year: Volume: Issue: Page: Find

 Mat. Sb., 2007, Volume 198, Number 5, Pages 33–44 (Mi msb1110)

Special factorization of a non-invertible integral Fredholm operator of the second kind with Hilbert–Schmidt kernel

G. A. Grigoryan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: The problem of the special factorization of a non-invertible integral Fredholm operator $I-K$ of the second kind with Hilbert–Schmidt kernel is considered. Here $I$ is the identity operator and $K$ is an integral operator:
$$(Kf)(x)\equiv\int_0^1 \mathrm K(x,t)f(t) dt, \qquad f \in L_2[0,1].$$

It is proved that $\lambda=1$ is an eigenvalue of $K$ of multiplicity $n\ge1$ if and only if $I-K=W_{+,1}\circ…\circ W_{+,n}\circ (I-K_n)\circ W_{-,1}\circ…\circ W_{-,n}$, where the $W_{+,j}$, $W_{-,j}$, $j=1,…,n$, are bounded operators in $L_2[0,1]$ of a special structure that are invertible from the left and the right, respectively.
Bibliography: 7 titles.

DOI: https://doi.org/10.4213/sm1110

Full text: PDF file (438 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2007, 198:5, 627–637

Bibliographic databases:

UDC: 517.968
MSC: 47G10, 47A68

Citation: G. A. Grigoryan, “Special factorization of a non-invertible integral Fredholm operator of the second kind with Hilbert–Schmidt kernel”, Mat. Sb., 198:5 (2007), 33–44; Sb. Math., 198:5 (2007), 627–637

Citation in format AMSBIB
\Bibitem{Gri07} \by G.~A.~Grigoryan \paper Special factorization of a~non-invertible integral Fredholm operator of the second kind with Hilbert--Schmidt kernel \jour Mat. Sb. \yr 2007 \vol 198 \issue 5 \pages 33--44 \mathnet{http://mi.mathnet.ru/msb1110} \crossref{https://doi.org/10.4213/sm1110} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2354285} \zmath{https://zbmath.org/?q=an:1165.47015} \elib{https://elibrary.ru/item.asp?id=9512209} \transl \jour Sb. Math. \yr 2007 \vol 198 \issue 5 \pages 627--637 \crossref{https://doi.org/10.1070/SM2007v198n05ABEH003852} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000249041900002} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548572413} 

• http://mi.mathnet.ru/eng/msb1110
• https://doi.org/10.4213/sm1110
• http://mi.mathnet.ru/eng/msb/v198/i5/p33

 SHARE:

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. G. A. Grigoryan, “On a Criterion for the Invertibility of Integral Operators of the Second Kind in the Space of Summable Functions on the Semiaxis”, Math. Notes, 96:6 (2014), 914–920
•  Number of views: This page: 367 Full text: 121 References: 43 First page: 7