Integral equations of the third kind with unbounded operators
- Authors: Korotkov V.B.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 58, No 2 (2017)
- Pages: 255-263
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171067
- DOI: https://doi.org/10.1134/S0037446617020070
- ID: 171067
Cite item
Abstract
We consider linear functional equations of the third kind in L2 with arbitrary measurable coefficients and unbounded integral operators with kernels satisfying broad conditions. We propose methods for reducing these equations by linear continuous invertible transformations either to equivalent integral equations of the first kind with nuclear operators or to equivalent integral equations of the second kind with quasidegenerate Carleman kernels. To the integral equations obtained after the reduction, one can apply various exact and approximate methods of solution; in particular, the two approximate methods developed in this article.
About the authors
V. B. Korotkov
Sobolev Institute of Mathematics
Author for correspondence.
Email: smj@math.nsc.ru
Russian Federation, Novosibirsk