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Expansion in the system of shifts of a B-spline

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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.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    S. M. Lytkin

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  1. S. M. Lytkin
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Correspondence to S. M. Lytkin.

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Original Russian Text © S. M. Lytkin, 2009, published in Matematicheskie Zametki, 2009, Vol. 86, No. 6, pp. 859–869.

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Lytkin, S.M. Expansion in the system of shifts of a B-spline. Math Notes 86, 801–810 (2009). https://doi.org/10.1134/S0001434609110224

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  • DOI: https://doi.org/10.1134/S0001434609110224

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