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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 323, Pages 213–223
DOI: https://doi.org/10.4213/tm4359 (Mi tm4359) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On Universal Sampling Recovery in the Uniform Norm

V. N. Temlyakovabcd

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Lomonosov Moscow State University, Moscow, 119991 Russia
c Moscow Center for Fundamental and Applied Mathematics, Moscow, 119991 Russia
d University of South Carolina, Columbia, SC 29208, USA
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DOI: https://doi.org/10.4213/tm4359
Abstract: It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol'skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions of two variables, where the Fibonacci point sets are used for recovery.
Keywords: sampling discretization, universality, recovery.
Funding agency Grant number
Russian Science Foundation 23-71-30001
This work was supported by the Russian Science Foundation under grant no. 23-71-30001, https://rscf.ru/en/project/23-71-30001/, and performed at Lomonosov Moscow State University.
Received: May 17, 2023
Revised: July 16, 2023
Accepted: July 20, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 323, Pages 206–216
DOI: https://doi.org/10.1134/S0081543823050139
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: Primary 65J05; Secondary 42A05, 65D30, 41A63
Language: Russian
Citation: V. N. Temlyakov, “On Universal Sampling Recovery in the Uniform Norm”, Theory of Functions of Several Real Variables and Its Applications, Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday, Trudy Mat. Inst. Steklova, 323, Steklov Mathematical Institute of RAS, Moscow, 2023, 213–223; Proc. Steklov Inst. Math., 323 (2023), 206–216
Citation in format AMSBIB
\Bibitem{Tem23}
\by V.~N.~Temlyakov
\paper On Universal Sampling Recovery in the Uniform Norm
\inbook Theory of Functions of Several Real Variables and Its Applications
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 323
\pages 213--223
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4359}
\crossref{https://doi.org/10.4213/tm4359}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4716524}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 323
\pages 206--216
\crossref{https://doi.org/10.1134/S0081543823050139}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85186913339}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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