On systems of linear functional equations of the second kind in L2
- Authors: Korotkov V.B.1
-
Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 58, No 5 (2017)
- Pages: 845-849
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171460
- DOI: https://doi.org/10.1134/S0037446617050111
- ID: 171460
Cite item
Abstract
We consider a general system of functional equations of the second kind in L2 with a continuous linear operator T satisfying the condition that zero lies in the limit spectrum of the adjoint operator T*. We show that this condition holds for the operators of a wide class containing, in particular, all integral operators. The system under study is reduced by means of a unitary transformation to an equivalent system of linear integral equations of the second kind in L2 with Carleman matrix kernel of a special kind. By a linear continuous invertible change, this system is reduced to an equivalent integral equation of the second kind in L2 with quasidegenerate Carleman kernel. It is possible to apply various approximate methods of solution for such an equation.
About the authors
V. B. Korotkov
Sobolev Institute of Mathematics
Author for correspondence.
Email: smj@math.nsc.ru
Russian Federation, Novosibirsk
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