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Dal'nevostochnyi Matematicheskii Zhurnal, 2012, Volume 12, Number 2, Pages 255–261
(Mi dvmg244)
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This article is cited in 2 scientific papers (total in 2 papers)
A Kernel Smoothing Method for General Integral Equations
I. M. Novitskii Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Abstract:
In this paper, we reduce the general linear integral equation of the third kind
in $L^2(Y,\mu)$, with largely arbitrary kernel and coefficient, to an equivalent
integral equation either of the second kind or of the first kind in
$L^2(\mathbb{R})$, with the kernel being the linear pencil of bounded infinitely
differentiable bi-Carleman kernels expandable in absolutely and uniformly
convergent bilinear series. The reduction is done by using unitary equivalence
transformations.
Key words:
linear integral equations of the first, second, and third kind, unitary operator, multiplication operator, bi-integral operator, bi-Carleman kernel, Hilbert-Schmidt kernel, bilinear series expansions of kernels.
Received: 15.08.2012
Citation:
I. M. Novitskii, “A Kernel Smoothing Method for General Integral Equations”, Dal'nevost. Mat. Zh., 12:2 (2012), 255–261
Linking options:
https://www.mathnet.ru/eng/dvmg244 https://www.mathnet.ru/eng/dvmg/v12/i2/p255
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Statistics & downloads: |
Abstract page: | 269 | Full-text PDF : | 102 | References: | 47 | First page: | 1 |
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