Boundary criterion for integral operators
- Authors: Kal’menov T.S.1, Otelbaev M.1
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Affiliations:
- Institute of Mathematics and Mathematical Modeling
- Issue: Vol 93, No 1 (2016)
- Pages: 58-61
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/223372
- DOI: https://doi.org/10.1134/S1064562416010208
- ID: 223372
Cite item
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 ⊂ Rn 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.
About the authors
T. Sh. Kal’menov
Institute of Mathematics and Mathematical Modeling
Author for correspondence.
Email: kalmenov.t@mail.ru
Kazakhstan, ul. Shevchenko 28, Almaty, 050010
M. Otelbaev
Institute of Mathematics and Mathematical Modeling
Email: kalmenov.t@mail.ru
Kazakhstan, ul. Shevchenko 28, Almaty, 050010