Far Eastern Mathematical Journal

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A Kernel Smoothing Method for General Integral Equations

I. M. Novitskii

2012, issue 2, P. 255–261

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.

Keywords: 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

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References

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