This article is cited in 2 scientific papers (total in 2 papers)
Linear functional equations of the first, second, and third kind in $L_2$
V. B. Korotkov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Under consideration are the functional equations of the first, second, and third kind with operators in wide classes of linear continuous operators in $L_2$ containing all integral operators. We propose methods for reducing these equations by linear invertible changes either to linear integral equations of the first kind with nuclear operators or to equivalent linear integral equations of the second kind with quasidegenerate Carleman kernels. Some various approximate methods of solution are applicable to the so-obtained integral equations.
linear functional equation of the first, second and third kind in $L_2$, almost compact operator, integral operator, Carleman integral operator, Hilbert–Schmidt operator, nuclear operator, kernel, quasidegenerate kernel, degenerate kernel.
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Siberian Mathematical Journal, 2013, 54:6, 1029–1036
V. B. Korotkov, “Linear functional equations of the first, second, and third kind in $L_2$”, Sibirsk. Mat. Zh., 54:6 (2013), 1294–1303; Siberian Math. J., 54:6 (2013), 1029–1036
Citation in format AMSBIB
\paper Linear functional equations of the first, second, and third kind in $L_2$
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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This publication is cited in the following articles:
V. B. Korotkov, “On systems of linear functional equations of the third kind in $L_2$”, Siberian Math. J., 56:3 (2015), 435–441
V. B. Korotkov, “Integral equations of the third kind with unbounded operators”, Siberian Math. J., 58:2 (2017), 255–263
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