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 Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 8–37 (Mi tm3533)

Nonlinear approximations of classes of periodic functions of many variables

D. B. Bazarkhanov

Institute of Mathematics, Almaty, Kazakhstan

Abstract: Order-sharp estimates are established for the best $N$-term approximations of functions in the classes $\mathrm B^{sm}_{pq}(\mathbb T^k)$ and $\mathrm L^{sm}_{pq}(\mathbb T^k)$ of Nikol'skii–Besov and Lizorkin–Triebel types with respect to the multiple system $\widetilde {\mathcal W}^m$ of Meyer wavelets in the metric of $L_r(\mathbb T^k)$ for various relations between the parameters $s,p,q,r$, and $m$ ($s=(s_1,…,s_n)\in\mathbb R^n_+$, $1\leq p,q,r\leq\infty$, $m=(m_1,…,m_n)\in\mathbb N^n$, and $k=m_1+…+m_n$). The proof of upper estimates is based on variants of the so-called greedy algorithms.

DOI: https://doi.org/10.1134/S0371968514010026

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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 2–31

Bibliographic databases:

UDC: 517.518.8

Citation: D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 8–37; Proc. Steklov Inst. Math., 284 (2014), 2–31

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tm3533
• https://doi.org/10.1134/S0371968514010026
• http://mi.mathnet.ru/eng/tm/v284/p8

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Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Sh. A. Balgimbayeva, “Nonlinear approximation of function spaces of mixed smoothness”, Siberian Math. J., 56:2 (2015), 262–274
2. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36
3. S. Balgimbayeva, T. Smirnov, “Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothnes”, Anal. Math., 43:1 (2017), 1–26
4. D. B. Bazarkhanov, “Sparse approximation of some function classes with respect to multiple Haar system on the unit cube”, International conference functional analysis in interdisciplinary applications (FAIA 2017), AIP Conf. Proc., 1880, ed. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 030017
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