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Mat. Sb., 2006, Volume 197, Number 1, Pages 71–96 (Mi msb1496)  

This article is cited in 9 scientific papers (total in 9 papers)

Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Precise (in order) estimates of the Kolmogorov widths in the space $L_q$, $1<q<\infty$, of the classes $B^r_{1,\theta}$ and $B^r_{\infty,\theta}$ and also of the trigonometric widths of the classes $B^r_{p,\theta}$ in $L_q$ for $p$ and $q$ satisfying certain relations are obtained.
Bibliography: 18 titles.

DOI: https://doi.org/10.4213/sm1496

Full text: PDF file (532 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:1, 69–93

Bibliographic databases:

UDC: 517.5
MSC: 46E35
Received: 15.10.2004 and 14.07.2005

Citation: A. S. Romanyuk, “Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions”, Mat. Sb., 197:1 (2006), 71–96; Sb. Math., 197:1 (2006), 69–93

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v197/i1/p71

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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. M.S. Sgibnev, “Semimultiplicative moments of factors in Wiener-Hopf matrix factorization”, Sb. Math, 199:2 (2008), 277  mathnet  crossref  mathscinet  zmath  elib  scopus
    3. Romanyuk A.S., Romanyuk V.S., “Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables”, Ukr. Math. J., 62:4 (2010), 612–629  crossref  mathscinet  zmath  isi  scopus
    4. Romanyuk A.S., “Poperechniki i nailuchshee priblizhenie klassov $B^r_{p,\theta}$ periodicheskikh funktsii mnogikh peremennykh”, Anal. Math., 37:3 (2011), 181–213  crossref  mathscinet  zmath  isi  scopus
    5. Derev'yanko N.V., “Trigonometric Widths of Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 64:8 (2013), 1185–1198  crossref  mathscinet  zmath  isi  scopus
    6. Akishev G., “Trigonometric Widths of the Nikol'Skii-Besov Classes in the Lebesgue Space With Mixed Norm”, Ukr. Math. J., 66:6 (2014), 807–817  crossref  mathscinet  zmath  isi  scopus
    7. G. A. Akishev, “Estimates for Kolmogorov widths of the Nikol'skii — Besov — Amanov classes in the Lorentz space”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 1–12  mathnet  crossref  mathscinet  elib
    8. Myronyuk V.V., “Trigonometric Approximations and Kolmogorov Widths of Anisotropic Besov Classes of Periodic Functions of Several Variables”, Ukr. Math. J., 66:8 (2015), 1248–1266  crossref  mathscinet  zmath  isi  scopus
    9. 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
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