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Mat. Zametki, 2010, Volume 87, Issue 1, Pages 108–121 (Mi mz4053)  

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

Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$

S. A. Stasyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We obtain order-sharp estimates of best approximation for the classes $B^\Omega_{p,\theta}$ of periodic functions of several variables by trigonometric polynomials whose spectra are generated by the level surfaces of the function $\Omega(t)$.

Keywords: periodic function of several variables, trigonometric polynomial, level surface, Bari–Stechkin condition, Vallée-Poussin kernel, modulus of continuity, Hölder'd inequality

DOI: https://doi.org/10.4213/mzm4053

Full text: PDF file (510 kB)
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English version:
Mathematical Notes, 2010, 87:1, 102–114

Bibliographic databases:

UDC: 517.51
Received: 22.05.2007

Citation: S. A. Stasyuk, “Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$”, Mat. Zametki, 87:1 (2010), 108–121; Math. Notes, 87:1 (2010), 102–114

Citation in format AMSBIB
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\jour Mat. Zametki
\yr 2010
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\pages 108--121
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\vol 87
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\pages 102--114
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  • http://mi.mathnet.ru/eng/mz/v87/i1/p108

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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, “Nailuchshee priblizhenie periodicheskikh funktsii neskolkikh peremennykh iz klassov $MB^\omega_{p,\theta}$ v ravnomernoi metrike”, Tr. IMM UrO RAN, 18, no. 4, 2012, 258–266  mathnet  elib
    2. Stasyuk S.A., “Best approximation of periodic functions of several variables from the classes $MB_{p,\theta}^\omega$”, Ukrainian Math. J., 64:1 (2012), 156–161  crossref  zmath  isi  elib  scopus
    3. S. A. Stasyuk, “Priblizhenie summami Fure i kolmogorovskie poperechniki klassov $\mathbf{MB}^\Omega_{p,\theta}$ periodicheskikh funktsii neskolkikh peremennykh”, Tr. IMM UrO RAN, 20, no. 1, 2014, 247–257  mathnet  mathscinet  elib
    4. Derev'yanko N.V., “Approximation of the Classes $H_p^\omega$ of Periodic Functions of Many Variables in the Space $L_p$”, Ukr. Math. J., 66:5 (2014), 707–718  crossref  mathscinet  zmath  isi  scopus
    5. Sh. A. Balgimbaeva, T. I. Smirnov, “Otsenki poperechnikov Fure klassov periodicheskikh funktsii so smeshannym modulem gladkosti”, Tr. IMM UrO RAN, 21, no. 4, 2015, 78–94  mathnet  mathscinet  elib
    6. Stasyuk S.A. Yanchenko S.Ya., “Approximation of Functions From Nikolskii-Besov Type Classes of Generalized Mixed Smoothness”, Anal. Math., 41:4 (2015), 311–334  crossref  mathscinet  zmath  isi  scopus
    7. Yanchenko S.Ya., “Order Estimates For the Approximating Characteristics of Functions From the Classes With a Given Majorant of Mixed Modules of Continuity in the Uniform Metric”, Ukr. Math. J., 68:12 (2017), 1975–1985  crossref  mathscinet  isi  scopus
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