Geodesic
A Kernel Smoothing Method for General Integral Equations
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 255-261

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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. 
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     author = {I. M. Novitskii},
     title = {A {Kernel} {Smoothing} {Method} for {General} {Integral} {Equations}},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {255--261},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a10/}
}
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I. M. Novitskii. A Kernel Smoothing Method for General Integral Equations. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 2, pp. 255-261. http://geodesic.mathdoc.fr/item/DVMG_2012_12_2_a10/