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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 2, Pages 69–98 (Mi izv558)  

This article is cited in 5 scientific papers (total in 5 papers)

Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B_{p, \theta}^r$

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We obtain order-sharp estimates for bilinear approximations of periodic functions of $2d$ variables of the form $f(x,y)=f(x-y)$, $x, y\in \pi_d = \prod_{j=1}^d[-\pi, \pi]$, obtained from functions $f(x)\in B_{p, \theta}^r$, $1\le p<\infty$, by translating the argument $x\in \pi_d$ by vectors $y\in \pi_d$. We also study the deviations of step hyperbolic Fourier sums on the classes $B_{1, \theta}^r$ and the best orthogonal trigonometric approximations in $L_q$, $ 1<q<\infty$, of functions belonging to these classes.

DOI: https://doi.org/10.4213/im558

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English version:
Izvestiya: Mathematics, 2006, 70:2, 277–306

Bibliographic databases:

UDC: 517.5
MSC: 42B99, 41A46, 41A50
Received: 08.05.2003

Citation: A. S. Romanyuk, “Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B_{p, \theta}^r$”, Izv. RAN. Ser. Mat., 70:2 (2006), 69–98; Izv. Math., 70:2 (2006), 277–306

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 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
    2. K. A. Bekmaganbetov, “O poryadkakh priblizheniya klassa Besova v metrike anizotropnykh prostranstv Lorentsa”, Ufimsk. matem. zhurn., 1:2 (2009), 9–16  mathnet  zmath  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, “Best Trigonometric and Bilinear Approximations of Classes of Functions of Several Variables”, Math. Notes, 94:3 (2013), 379–391  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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