Loading [MathJax]/jax/output/SVG/config.js
Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
\Bibitem{Tem21}
\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
\mathnet{http://mi.mathnet.ru/tm4133}
\crossref{https://doi.org/10.4213/tm4133}
\elib{https://elibrary.ru/item.asp?id=46045491}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 270--281
\crossref{https://doi.org/10.1134/S0081543821010181}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000642515300018}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85104615318}
Linking options:
  • https://www.mathnet.ru/eng/tm4133
  • https://doi.org/10.4213/tm4133
  • https://www.mathnet.ru/eng/tm/v312/p282
    • This publication is cited in the following 7 articles:
    1. Oksana V. Germider, Vasily N. Popov, “On calculation of bending of a thin orthotropic plate using Legendre and Chebyshev polynomials of the first kind”, Zhurn. SFU. Ser. Matem. i fiz., 17:5 (2024), 586–598  mathnet
    2. F. Dai, V. N. Temlyakov, “Sampling Discretization of Integral Norms and Its Application”, Proc. Steklov Inst. Math., 319 (2022), 97–109  mathnet  crossref  crossref  mathscinet
    3. Egor D. Kosov, “Remarks on Sampling Discretization of Integral Norms of Functions”, Proc. Steklov Inst. Math., 319 (2022), 189–199  mathnet  crossref  crossref  mathscinet
    4. Vladimir N. Temlyakov, Tino Ullrich, “Approximation of functions with small mixed smoothness in the uniform norm”, J. Approx. Theory, 277 (2022), 105718–23  mathnet  crossref
    5. B. Kashin, E. Kosov, I. Limonova, V. Temlyakov, “Sampling discretization and related problems”, J. Complexity, 71 (2022), 101653–55  mathnet  crossref  scopus
    6. Kosov E.D., “Marcinkiewicz-Type Discretization of l-P-Norms Under the Nikolskii-Type Inequality Assumption”, J. Math. Anal. Appl., 504:1 (2021), 125358  crossref  mathscinet  isi
    7. Temlyakov V., Ullrich T., “Bounds on Kolmogorov Widths and Sampling Recovery For Classes With Small Mixed Smoothness”, J. Complex., 67 (2021), 101575  crossref  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:401
    Full-text PDF :71
    References:62
    First page:15
     
      Contact us:
    math-net2025_04@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025