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Approximation of functions of several variables by linear methods in the space Sp

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Abstract

In the spaces Sp of functions of several variables, 2π-periodic in each variable, we study the approximative properties of operators A Δϱ,r and P Δϱ,s , which generate two summation methods of multiple Fourier series on triangular regions. In particular, in the terms of approximation estimates of these operators, we give a constructive description of classes of functions, whose generalized derivatives belong to the classes SpHω.

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Authors and Affiliations

  1. Department of Theory of Functions, Institute of Mathematics of Ukrainian National Academy of Sciences, 3, Tereshchenkivska st., Kiev, Ukraine, 01601

    Viktor V. Savchuk & Andriy L. Shidlich

Authors
  1. Viktor V. Savchuk
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  2. Andriy L. Shidlich
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Correspondence to Viktor V. Savchuk.

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Communicated by L. Kérchy

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Savchuk, V.V., Shidlich, A.L. Approximation of functions of several variables by linear methods in the space Sp. ActaSci.Math. 80, 477–489 (2014). https://doi.org/10.14232/actasm-012-837-8

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  • DOI: https://doi.org/10.14232/actasm-012-837-8

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