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Approximation of the Besov classes of periodic functions of several variables in a space Lq

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Abstract

Order estimates are obtained for best approximations by polynomials constructed according to hyperbolic crosses on the classes B rp , θ of periodic functions of several variables. The order is found of the Kolmogorov width on these classes in the spaces Lq for 1 <p ⩽q ⩽2.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukraine, Kiev

    A. S. Romanyuk

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  1. A. S. Romanyuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1398–1408, October, 1991.

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Romanyuk, A.S. Approximation of the Besov classes of periodic functions of several variables in a space Lq . Ukr Math J 43, 1297–1306 (1991). https://doi.org/10.1007/BF01061817

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  • DOI: https://doi.org/10.1007/BF01061817

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