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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 Universitya
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
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. 17-28.
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