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Mat. Sb., 2004, Volume 195, Number 2, Pages 91–116 (Mi msb801)  

This article is cited in 14 scientific papers (total in 14 papers)

Approximability of the classes $B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Several questions of the approximability by linear methods of the Besov classes $B_{1,\theta}^r$ and $B_{p,\theta}^r$ of periodic functions of several variables, $1\leqslant p<\infty$, are considered alongside their best approximations in the spaces $L_1$ and $L_\infty$, respectively. Taken for approximation aggregates are trigonometric polynomials with spectrum in the step hyperbolic cross. Sharp (in order) estimates of the deviations of step hyperbolic Fourier sums on the classes $B_{p,\theta}^r$, $1\leqslant p<\infty$, in the $L_\infty$ space are also obtained.

DOI: https://doi.org/10.4213/sm801

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English version:
Sbornik: Mathematics, 2004, 195:2, 237–261

Bibliographic databases:

UDC: 517.5
MSC: 41A35, 46E35
Received: 12.11.2002

Citation: A. S. Romanyuk, “Approximability of the classes $B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations”, Mat. Sb., 195:2 (2004), 91–116; Sb. Math., 195:2 (2004), 237–261

Citation in format AMSBIB
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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. A. S. Romanyuk, “Best Trigonometric Approximations for Some Classes of Periodic Functions of Several Variables in the Uniform Metric”, Math. Notes, 82:2 (2007), 216–228  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Sb. Math., 199:2 (2008), 253–275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. S. A. Stasyuk, “Best Approximations of Periodic Functions of Several Variables from the Classes $B^\Omega_{p,\theta}$”, Math. Notes, 87:1 (2010), 102–114  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. S. Romanyuk, “Approximation of Classes $B^r_{p,\theta}$ of Periodic Functions of One and Several Variables”, Math. Notes, 87:3 (2010), 403–415  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Sickel W., Ullrich T., “Spline interpolation on sparse grids”, Appl Anal, 90:3–4 (2011), 337–383  crossref  mathscinet  zmath  isi  elib
    6. Pomahiok A.C., “Diameters and best approximation of the classes B-p(r) of periodic functions of several variables”, Anal Math, 37:3 (2011), 181–213  crossref  mathscinet  isi
    7. N. N. Pustovoitov, “Approximation of periodic functions in the classes $H_q^\Omega$ by linear methods”, Sb. Math., 203:1 (2012), 88–110  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. 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
    9. Konograi A.F., “Approximation of Classes Bp, Theta (Omega) of Periodic Functions in Several Variables by Linear Methods”, Anal. Math., 39:3 (2013), 217–233  crossref  mathscinet  zmath  isi
    10. Yanchenko S.Ya., “Approximation of Functions From the Classes S (R) (P, Theta) B in the Uniform Metric”, Ukr. Math. J., 65:5 (2013), 771–779  crossref  mathscinet  zmath  isi
    11. Romanyuk A.S., “Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol'skii–Besov Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 67:11 (2016), 1739–1757  crossref  mathscinet  zmath  isi
    12. 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
    13. Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795  crossref  mathscinet  isi  scopus
    14. Romanyuk A.S., “Entropy Numbers and Widths For the Nikol'Skii-Besov Classes of Functions of Many Variables in the Space l-Infinity”, Anal. Math., 45:1 (2019), 133–151  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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