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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
$n\geqslant1$ if and only if
$I-K=W_{+,1}\circ\dots\circ W_{+,n}\circ (I-K_n)\circ
W_{-,1}\circ\dots\circ W_{-,n}$, where the $W_{+,j}$, $W_{-,j}$,
$j=1,\dots,n$, 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.
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
Linking options:
https://www.mathnet.ru/eng/sm1110https://doi.org/10.1070/SM2007v198n05ABEH003852 https://www.mathnet.ru/eng/sm/v198/i5/p33
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Abstract page: | 486 | Russian version PDF: | 236 | English version PDF: | 15 | References: | 57 | First page: | 7 |
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