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Mat. Zametki, 2007, Volume 82, Issue 2, Pages 247–261 (Mi mz3797)  

This article is cited in 7 scientific papers (total in 7 papers)

Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We study best $M$-term trigonometric approximations and best orthogonal trigonometric approximations for the classes $B^r_{p,\theta}$ and $W^r_{p,\alpha}$ of periodic functions of several variables in the uniform metric.

Keywords: best trigonometric approximation, the classes $B^r_{p,\theta}$ and $W^r_{p,\alpha}$ of periodic functions, Minkowski's inequality, Hölder's inequality, Vallée-Poussin kernel

DOI: https://doi.org/10.4213/mzm3797

Full text: PDF file (536 kB)
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English version:
Mathematical Notes, 2007, 82:2, 216–228

Bibliographic databases:

UDC: 517.5
Received: 28.03.2005
Revised: 17.11.2006

Citation: A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Mat. Zametki, 82:2 (2007), 247–261; Math. Notes, 82:2 (2007), 216–228

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v82/i2/p247

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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. Voitenko S.P., “Best $M$-Term trigonometric approximations of the classes $B_{p,\theta}^{\Omega}$ of periodic functions of many variables”, Ukrain. Math. J., 61:9 (2009), 1404–1416  crossref  mathscinet  isi  scopus
    2. Romanyuk A.S., Romanyuk V.S., “Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables”, Ukrain. Math. J., 62:4 (2010), 612–629  crossref  mathscinet  zmath  isi  scopus
    3. D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Proc. Steklov Inst. Math., 284 (2014), 2–31  mathnet  crossref  crossref  isi  elib  elib
    4. Serdyuk A.S., Stepanyuk T.A., “Order Estimates For the Best Orthogonal Trigonometric Approximations of the Classes of Convolutions of Periodic Functions of Low Smoothness”, Ukr. Math. J., 67:7 (2015), 1038–1061  crossref  mathscinet  zmath  isi  scopus
    5. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Shvai K.V., “the Best M-Term Trigonometric Approximations of Classes of (Psi,Beta)-Differentiable Periodic Multivariate Functions in the Space l-Beta,1(Psi)”, J. Numer. Appl. Math., 2:122 (2016), 83–91  isi
    7. Shkapa V.V., “Best Trigonometric and Bilinear Approximations for the Classes of (, )-Differentiable Periodic Functions”, Ukr. Math. J., 68:3 (2016), 433–447  crossref  mathscinet  isi  scopus
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