Abstract
Integral operators of the form \(L_K^{ - 1} f(x) = \int\limits_\Omega {K(x,t)f(t)dt}\) for the case of a finite domain Ω ⊂ R n with smooth boundary ∂Ω are considered. Conditions on the real kernel K(x, t) of an integral operator under which this operator satisfies a well-defined boundary condition for the corresponding differential equation are found. The application of the results is demonstrated on the example of a Sturm–Liouville equation, for which the derivation of the general form of well-posed boundary value problems is presented.
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Original Russian Text © T.Sh. Kal’menov, M. Otelbaev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 466, No. 4, pp. 395–398.
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Kal’menov, T.S., Otelbaev, M. Boundary criterion for integral operators. Dokl. Math. 93, 58–61 (2016). https://doi.org/10.1134/S1064562416010208
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DOI: https://doi.org/10.1134/S1064562416010208