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Russia Izhevsk
Section  Mathematics 
Title  Some problems of the theory of linear equations 
Author(s)  Islamov G.G.^{a} 
Affiliations  Udmurt State University^{a} 
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 finitedimensional 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'kiiFilippov 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 
UDC  517.929 
MSC  34K06, 65L03 
DOI  10.20537/vm130103 
Received  1 February 2013 
Language  Russian 
Citation  Islamov G.G. Some problems of the theory of linear equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2013, issue 1, pp. 1728. 
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