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This article is cited in 11 scientific papers (total in 11 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:
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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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Linking options:
http://mi.mathnet.ru/eng/msb1496https://doi.org/10.4213/sm1496 http://mi.mathnet.ru/eng/msb/v197/i1/p71
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This publication is cited in the following articles:
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A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Sb. Math., 199:2 (2008), 253–275
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M.S. Sgibnev, “Semimultiplicative moments of factors in Wiener-Hopf matrix factorization”, Sb. Math, 199:2 (2008), 277
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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
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Romanyuk A.S., “Poperechniki i nailuchshee priblizhenie klassov $B^r_{p,\theta}$ periodicheskikh funktsii mnogikh peremennykh”, Anal. Math., 37:3 (2011), 181–213
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Derev'yanko N.V., “Trigonometric Widths of Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 64:8 (2013), 1185–1198
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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
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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
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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
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Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795
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Cobos F., Kuehn T., Sickel W., “On Optimal Approximation in Periodic Besov Spaces”, J. Math. Anal. Appl., 474:2 (2019), 1441–1462
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Bekmaganbetov K.A., Toleugazy Y., “On the Order of the Trigonometric Diameter of the Anisotropic Nikol'Skii-Besov Class in the Metric of Anisotropic Lorentz Spaces”, Anal. Math., 45:2 (2019), 237–247
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