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Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 251–260 (Mi timm1246)  

This article is cited in 2 scientific papers (total in 2 papers)

Approximation of certain smoothness classes of periodic functions of several variables by polynomials with regard to the tensor Haar system

S. A. Stasyuk

Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev

Abstract: We investigate two kinds of approximation (linear and nonlinear) of certain smoothness classes (close to Nikol'skii-Besov type classes of mixed smoothness) of periodic functions of several variables by polynomials with regard to the tensor Haar system. For the functions of these classes we obtain upper order estimates for the approximation by step-hyperbolic Fourier-Haar sums and exact order estimates for the best $m$-term approximation with regard to the tensor Haar system.

Keywords: approximation of functions of several variables, tensor Haar system, best $m$-term approximation.

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Bibliographic databases:
UDC: 517.51

Citation: S. A. Stasyuk, “Approximation of certain smoothness classes of periodic functions of several variables by polynomials with regard to the tensor Haar system”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 251–260

Citation in format AMSBIB
\Bibitem{Sta15}
\by S.~A.~Stasyuk
\paper Approximation of certain smoothness classes of periodic functions of several variables by polynomials with regard to the tensor Haar system
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 4
\pages 251--260
\mathnet{http://mi.mathnet.ru/timm1246}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468447}
\elib{https://elibrary.ru/item.asp?id=25301002}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Stasyuk, “Konstruktivnye razrezhennye trigonometricheskie priblizheniya dlya klassov funktsii s nebolshoi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 247–253  mathnet  crossref  mathscinet  elib
    2. S. A. Stasyuk, “Razrezhennoe trigonometricheskoe priblizhenie klassov Besova funktsii s maloi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 23, no. 3, 2017, 244–252  mathnet  crossref  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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