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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 1, Pages 17–28 (Mi vuu360)  

MATHEMATICS

Some problems of the theory of linear equations

G. G. Islamov

Udmurt State University, Izhevsk, Russia

Abstract: There are considered the structural, approximated and spectral properties of Fredholm operators of index $n$ and $(-n)$, acting between Banach spaces $B$ and $D$, where $D$ is isomorphic to the direct sum of $B$ and finite-dimensional space $E$ of dimension $n$. There is demonstrated the role of S. M. Nikol'skii theorem on Fredholm operator in the study of these properties as well as in the issue of solvability equations with boundary inequalities. For boundary value problems which are uniquely solvable, in the case of a separable Hilbert space $B$, based on Schmidt decomposition for a compact operator a scheme of discretization is proposed, and it allows application of an abstract version of Ryaben'kii–Filippov theorem on the relationship of approximation, stability and convergence.

Keywords: reconstructive modelling, factorization of linear operators, minimal rank perturbations, minimal set of cyclic vectors, equations with boundary inequalities.

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UDC: 517.929
MSC: 34K06, 65L03
Received: 01.02.2013

Citation: G. G. Islamov, “Some problems of the theory of linear equations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1, 17–28

Citation in format AMSBIB
\Bibitem{Isl13}
\by G.~G.~Islamov
\paper Some problems of the theory of linear equations
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 1
\pages 17--28
\mathnet{http://mi.mathnet.ru/vuu360}


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  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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