Direct and inverse theorems in the theory of approximation by the Ritz method

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dc.creatorTorba, S. M.
dc.creatorGorbachuk, M. L.
dc.creatorGrushka, Ya. I.
dc.date2007-09-26
dc.date.accessioned2026-07-07T08:32:23Z
dc.date.available2026-07-07T08:32:23Z
dc.descriptionFor an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence to zero of its best approximation by exponential-type entire vectors of the operator $B$, and the $k$-modulus of continuity of the vector $x$ with respect to the operator $B$. The results are used for finding a priori estimates for the Ritz approximate solutions of operator equations in a Hilbert space.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0709.4243
dc.identifierhttp://arxiv.org/abs/0709.4243
dc.identifierM. L. Horbachuk, Ya. I. Hrushka, and S. M. Torba, "Direct and inverse theorems in the theory of approximation by the Ritz method", Ukr.Math.J., Vol. 57, No. 5, 2005, pp. 751-764
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138782
dc.subjectFunctional Analysis
dc.subject41A25, 41A17, 41A65
dc.titleDirect and inverse theorems in the theory of approximation by the Ritz method
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