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Matematicheskie Zametki, 2024, Volume 116, Issue 5, Pages 744–758
DOI: https://doi.org/10.4213/mzm14208 (Mi mzm14208) 		 
Reconstruction of functions in Sobolev- and Korobov-type $n$-ary classes with small smoothness parameters

A. D. Kashinaa, M. G. Plotnikovab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.4213/mzm14208
Abstract: The problems of exact and approximate reconstruction of integrable functions from their values on a set of small measure are considered. The classes of functions under consideration are the $p$-ary counterparts of the Sobolev and Korobov classes with small smoothness parameters.
Keywords: reconstruction of functions, Vilenkin–Chrestenson system, Fourier coefficient, Sobolev class, Korobov class.
Funding agency Grant number
Russian Science Foundation 23-71-30001
This work was financially supported by the Russian Science Foundation, project 23-71-30001, https://rscf.ru/en/project/23-71-30001/, at Lomonosov Moscow State University.
Received: 30.11.2023
Revised: 01.03.2024
English version:
Mathematical Notes, 2024, Volume 116, Issue 5, Pages 1000–1013
DOI: https://doi.org/10.1134/S0001434624110129
Document Type: Article
UDC: 517.518
MSC: 42C10, 41A30,
Language: Russian
Citation: A. D. Kashina, M. G. Plotnikov, “Reconstruction of functions in Sobolev- and Korobov-type $n$-ary classes with small smoothness parameters”, Mat. Zametki, 116:5 (2024), 744–758; Math. Notes, 116:5 (2024), 1000–1013
Citation in format AMSBIB
\Bibitem{KasPlo24}
\by A.~D.~Kashina, M.~G.~Plotnikov
\paper Reconstruction of functions in Sobolev- and Korobov-type $n$-ary classes with small smoothness parameters
\jour Mat. Zametki
\yr 2024
\vol 116
\issue 5
\pages 744--758
\mathnet{http://mi.mathnet.ru/mzm14208}
\crossref{https://doi.org/10.4213/mzm14208}
\transl
\jour Math. Notes
\yr 2024
\vol 116
\issue 5
\pages 1000--1013
\crossref{https://doi.org/10.1134/S0001434624110129}
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