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

This article is cited in 1 scientific paper (total in 1 paper)

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
Received: 04.07.2005 and 02.08.2006

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
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\by G.~A.~Grigoryan
\paper Special factorization of a~non-invertible integral Fredholm
operator of the second kind with
Hilbert--Schmidt kernel
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\vol 198
\issue 5
\pages 33--44
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\crossref{https://doi.org/10.4213/sm1110}
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\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}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34548572413}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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