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Matematicheskie Zametki, 2009, Volume 86, Issue 6, Pages 859–869
DOI: https://doi.org/10.4213/mzm4738 (Mi mzm4738) 		 
Expansion in the System of Shifts of a B-Spline

S. M. Lytkin

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm4738
Abstract: A method of approximating functions by linear combinations of shifts of a fixed function, a B-spline of the first, second, or third degree, is proposed. This method is exact for the classes of splines of the corresponding degree with deficiency 1. We obtain estimates of strong type for the norms of approximating operators in certain spaces, from which it follows immediately that the approximation in these spaces coincides in order with the best approximation by splines.
Keywords: spline, B-spline, periodic spline, system of shifts of a B-spline, deficiency of a spline, Hölder's inequality, Jensen's inequality.
Received: 03.04.2008
Revised: 13.04.2009
English version:
Mathematical Notes, 2009, Volume 86, Issue 6, Pages 801–810
DOI: https://doi.org/10.1134/S0001434609110224
Bibliographic databases:
UDC: 517.518
Language: Russian
Citation: S. M. Lytkin, “Expansion in the System of Shifts of a B-Spline”, Mat. Zametki, 86:6 (2009), 859–869; Math. Notes, 86:6 (2009), 801–810
Citation in format AMSBIB
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