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Best trigonometric and bilinear approximations of functions of several variables from the classes Bp,θr· I

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Abstract

Approximations are studied of the classes Bp,θr of periodic functions of several variables with the help of trigonometric polynomials with a given number of harmonics. The results obtained are used to establish order estimates of the approximation of functions of the form f(x−y), f(x) ε Bp,θr, by combinations of products of functions of a fewer number of variables.

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Authors and Affiliations

  1. Mathematics Institute, 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. 44, No. 11, pp. 1535–1547, November, 1992.

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Romanyuk, A.S. Best trigonometric and bilinear approximations of functions of several variables from the classes Bp,θr· I. Ukr Math J 44, 1411–1424 (1992). https://doi.org/10.1007/BF01071517

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  • DOI: https://doi.org/10.1007/BF01071517

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