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Tr. Mat. Inst. Steklova, 2016, Volume 293, Pages 8–42 (Mi tm3702)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear trigonometric approximations of multivariate function classes

D. B. Bazarkhanov

Institute of Mathematics and Mathematical Modeling, ul. Pushkina 125, Almaty, 050010 Kazakhstan

Abstract: Order-sharp estimates are established for the best $N$-term approximations of functions from Nikol'skii–Besov type classes $\mathrm B^{sm}_{pq}(\mathbb T^k)$ with respect to the multiple trigonometric system $\mathfrak T^{(k)}$ in the metric of $L_r(\mathbb T^k)$ for a number of relations between the parameters $s,p,q,r$, and $m$ ($s=(s_1,…,s_n)\in\mathbb R^n_+$, $1\leq p,q,r\leq\infty$, $m=(m_1,…,m_n)\in\mathbb N^n$, $k=m_1+…+m_n$). Constructive methods of nonlinear trigonometric approximation –variants of the so-called greedy algorithms – are used in the proofs of upper estimates.

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 5130/ГФ4
5129/ГФ4
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan, project nos. 5130/GF4 and 5129/GF4.


DOI: https://doi.org/10.1134/S0371968516020023

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 293, 2–36

Bibliographic databases:

UDC: 517.518.8
Received: December 2, 2015

Citation: D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 8–42; Proc. Steklov Inst. Math., 293 (2016), 2–36

Citation in format AMSBIB
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\paper Nonlinear trigonometric approximations of multivariate function classes
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 8--42
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. A. Stasyuk, “Konstruktivnye razrezhennye trigonometricheskie priblizheniya dlya klassov funktsii s nebolshoi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 247–253  mathnet  crossref  mathscinet  elib
    2. S. A. Stasyuk, “Razrezhennoe trigonometricheskoe priblizhenie klassov Besova funktsii s maloi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 23, no. 3, 2017, 244–252  mathnet  crossref  elib
    3. 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, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 030017  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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