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Russian Mathematical Surveys, 2019, Volume 74, Issue 4, Pages 579–630
DOI: https://doi.org/10.1070/RM9892 (Mi rm9892) 		 
This article is cited in 44 scientific papers (total in 44 papers)

Integral norm discretization and related problems

F. Daia, A. Prymakb, V. N. Temlyakovcde, S. Yu. Tikhonovfgh

a University of Alberta, Edmonton, Canada
b University of Manitoba, Winnipeg, Canada
c University of South Carolina, Columbia, USA
d Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
e Lomonosov Moscow State University
f Centre de Recerca Matemàtica, Barcelona, Spain
g ICREA, Barcelona, Spain
h Universitat Autònoma de Barcelona, Barcelona, Spain
English version PDF (887 kB) Citations (44) Russian version article
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DOI: https://doi.org/10.1070/RM9892
Abstract: The problem is discussed of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure. This problem is investigated for elements of finite-dimensional spaces. Also, discretization of the uniform norm of functions in a given finite-dimensional subspace of continuous functions is studied. Special attention is given to the case of multivariate trigonometric polynomials with frequencies (harmonics) in a finite set with fixed cardinality. Both new results and a survey of known results are presented.
Bibliography: 47 titles.
Keywords: trigonometric polynomials, discretization, Marcinkiewicz-type theorems.
Funding agency Grant number
Natural Sciences and Engineering Research Council of Canada (NSERC) RGPIN 04702-15
RGPIN 04863-15
Ministry of Education and Science of the Russian Federation 14.W03.31.0031
Ministerio de Ciencia e Innovación de España MTM 2017-87409-P
2017 SGR 358
Generalitat de Catalunya
The first author's research was partially supported by NSERC of Canada Discovery Grant RGPIN 04702-15. The second author's research was partially supported by NSERC of Canada Discovery Grant RGPIN 04863-15. The third author's research was supported by the Russian Federation Government Grant No. 14.W03.31.0031. The fourth author's research was partially supported by MTM 2017-87409-P, 2017 SGR 358, and the CERCA Programme of the Generalitat de Catalunya.
Received: 20.12.2018
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 65J05, 65D32, 41A55, 41A17, 41A63, 42A10, 42B99
Language: English
Original paper language: Russian
Citation: F. Dai, A. Prymak, V. N. Temlyakov, S. Yu. Tikhonov, “Integral norm discretization and related problems”, Russian Math. Surveys, 74:4 (2019), 579–630
Citation in format AMSBIB
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\by F.~Dai, A.~Prymak, V.~N.~Temlyakov, S.~Yu.~Tikhonov
\paper Integral norm discretization and related problems
\jour Russian Math. Surveys
\yr 2019
\vol 74
\issue 4
\pages 579--630
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    • This publication is cited in the following 44 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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