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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 282–293
DOI: https://doi.org/10.4213/tm4133 (Mi tm4133) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials

V. N. Temlyakovabcd

a University of South Carolina, Columbia, SC 29208, USA
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Lomonosov Moscow State University, Moscow, 119991 Russia
d Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
Full-text PDF (228 kB) Citations (7)
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DOI: https://doi.org/10.4213/tm4133
Abstract: The paper is devoted to discretization of integral norms of functions from a given finite-dimensional subspace. We use recent general results on sampling discretization to derive a new Marcinkiewicz type discretization theorem for the multivariate trigonometric polynomials with frequencies from the hyperbolic crosses. It is shown that recently developed techniques allow us to improve the known results in this direction.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
The work was supported by the Government of the Russian Federation, grant no. 14.W03.31.0031.
Received: May 16, 2020
Revised: September 1, 2020
Accepted: October 1, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 270–281
DOI: https://doi.org/10.1134/S0081543821010181
Bibliographic databases:
Document Type: Article
UDC: 517.518.83+517.518.87
Language: Russian
Citation: V. N. Temlyakov, “Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 282–293; Proc. Steklov Inst. Math., 312 (2021), 270–281
Citation in format AMSBIB
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\by V.~N.~Temlyakov
\paper Sampling Discretization of Integral Norms of the Hyperbolic Cross Polynomials
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 282--293
\publ Steklov Math. Inst.
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4133}
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\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 270--281
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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