È. M. Galeev, “Linear widths of Hölder–Nikol'skii classes of periodic functions of several variables”, Mat. Zametki, 59:2 (1996), 189–199; Math. Notes, 59:2 (1996), 133

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Matematicheskie Zametki, 1996, Volume 59, Issue 2, Pages 189–199
DOI: https://doi.org/10.4213/mzm1706 (Mi mzm1706)

This article is cited in 22 scientific papers (total in 22 papers)

Linear widths of Hölder–Nikol'skii classes of periodic functions of several variables

È. M. Galeev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (201 kB) Citations (22)

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DOI: https://doi.org/10.4213/mzm1706

Abstract: We consider the linear widths

$\lambda_N\bigl(W_p^r(T^n),L_q\bigr)$ and

$\lambda_N\bigl(H_p^r(T^n),L_q\bigr)$ of the classes

$W_p^r(T^n)$ and

$H_p^r(T^n)$ of periodic functions of one or several variables in the space

$L_q$ . For the Sobolev classes

$W_p^r(T^n)$ of functions of one or several variables, we state some well-known results without proof; for the Hölder–Nikol'skii classes

$H_p^r(T^n)$ , we state some well-known results, prove some new results, and present some previously unpublished proofs.

Received: 23.03.1995

English version:
Mathematical Notes, 1996, Volume 59, Issue 2, Pages 133–140
DOI: https://doi.org/10.1007/BF02310952

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: È. M. Galeev, “Linear widths of Hölder–Nikol'skii classes of periodic functions of several variables”, Mat. Zametki, 59:2 (1996), 189–199; Math. Notes, 59:2 (1996), 133–140

Citation in format AMSBIB

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\paper Linear widths of H\"older--Nikol'skii classes of periodic functions of several variables

\jour Mat. Zametki

\yr 1996

\vol 59

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\pages 189--199

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\transl

\jour Math. Notes

\yr 1996

\vol 59

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\crossref{https://doi.org/10.1007/BF02310952}

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Linking options:

https://www.mathnet.ru/eng/mzm1706

https://doi.org/10.4213/mzm1706

https://www.mathnet.ru/eng/mzm/v59/i2/p189

This publication is cited in the following 22 articles:

G. A. Akishev, “Ob otsenkakh lineinykh poperechnikov klassov funktsii mnogikh peremennykh v prostranstve Lorentsa”, Tr. IMM UrO RAN, 28, no. 4, 2022, 23–39
Dinh Dung, “B-Spline Quasi-Interpolation Sampling Representation and Sampling Recovery in Sobolev Spaces of Mixed Smoothness”, Acta Math. Vietnam, 43:1 (2018), 83–110
Dirksen S., Ullrich T., “Gelfand Numbers Related to Structured Sparsity and Besov Space Embeddings With Small Mixed Smoothness”, J. Complex., 48 (2018), 69–102
Yu. V. Malykhin, K. S. Ryutin, “The Product of Octahedra is Badly Approximated in the $\ell_{2,1}$-Metric”, Math. Notes, 101:1 (2017), 94–99
Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795
Byrenheid G., Ullrich T., “Optimal Sampling Recovery of Mixed Order Sobolev Embeddings Via Discrete Littlewood-Paley Type Characterizations”, Anal. Math., 43:2 (2017), 133–191
Van Kien Nguyen Sickel W., “Weyl Numbers of Embeddings of Tensor Product Besov Spaces”, J. Approx. Theory, 200 (2015), 170–220
Derev'yanko N.V., “Estimations of Linear Widths of the Classes $B_{p,\theta}^\Omega$ of Periodic Functions of Many Variables in the Space $L_q$”, Ukr. Math. J., 66:7 (2014), 1013–1027
Romanyuk A.S., “On the Problem of Linear Widths of the Classes $B_{p,\theta}^r$ of Periodic Functions of Many Variables”, Ukr. Math. J., 66:7 (2014), 1085–1098
Hansen M. Sickel W., “Best M-Term Approximation and Sobolev-Besov Spaces of Dominating Mixed Smoothness-the Case of Compact Embeddings”, Constr. Approx., 36:1 (2012), 1–51
E. M. Galeev, “Poperechniki funktsionalnykh klassov i konechnomernykh mnozhestv”, Vladikavk. matem. zhurn., 13:2 (2011), 3–14
Dinh Dung, “B-Spline Quasi-Interpolant Representations and Sampling Recovery of Functions with Mixed Smoothness”, J. Complex., 27:6 (2011), 541–567
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
Bazarkhanov D.B., “Otsenki poperechnikov klassov periodicheskikh funktsii mnogikh peremennykh”, Doklady Akademii nauk, 436:5 (2011), 583–585
D. B. Bazarkhanov, “Estimates for the widths of classes of periodic functions of several variables – I”, Eurasian Math. J., 1:3 (2010), 11–26
K. A. Bekmaganbetov, “O poryadkakh priblizheniya klassa Besova v metrike anizotropnykh prostranstv Lorentsa”, Ufimsk. matem. zhurn., 1:2 (2009), 9–16
Fang, GS, “The complexity of function approximation on Sobolev spaces with bounded mixed derivative by linear Monte Carlo methods”, Journal of Complexity, 24:3 (2008), 398
A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Sb. Math., 199:2 (2008), 253–275
G. A. Akishev, “On Orders of Approximation of Function Classes in Lorentz spaces with Anisotropic Norm”, Math. Notes, 81:1 (2007), 3–14
G. A. Akishev, “Approximation of function classes in spaces with mixed norm”, Sb. Math., 197:8 (2006), 1121–1144

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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