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Approximation of\((\bar \psi ,\bar \beta )\)-differentiable periodic functions of many variables

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Abstract

Best-approximation estimates are obtained in the integral and uniform metric on classes of periodic functions of many variables, which are defined by restrictions imposed on the mixed generalized derivative introduced by Stepanets. In this case, theharmonic of trigonometric polynomials, which are used for approximation of the classes of functions under consideration, are taken from the so-called hyperbolic crosses.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    P. V. Zaderei

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  1. P. V. Zaderei
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 367–377, March, 1993.

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Zaderei, P.V. Approximation of\((\bar \psi ,\bar \beta )\)-differentiable periodic functions of many variables. Ukr Math J 45, 389–401 (1993). https://doi.org/10.1007/BF01061011

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  • DOI: https://doi.org/10.1007/BF01061011

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