Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Akishev G. On estimates of the best M-term approximations of functions of many variables in a space with a uniform metric. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 2, pp. 154-166. DOI: 10.18500/1816-9791-2025-25-2-154-166, EDN: CQAXPK

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.05.2025
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.51
DOI: 
10.18500/1816-9791-2025-25-2-154-166
EDN: 
CQAXPK

On estimates of the best M-term approximations of functions of many variables in a space with a uniform metric

Autors: 
Akishev Gabdolla, Kazakhstan Branch of Lomonosov Moscow State University
Abstract: 

The paper considers the space of continuous functions with a uniform metric and the anisotropic Lorentz – Zygmund space of periodic functions of many variables and the Nikol’skii – Besov class in this space. We have established estimates of the best M-term trigonometric approximations of functions from the Nikol’skii – Besov class in a uniform metric.

Key words: 
uniform metric
Lorentz – Zygmund space
Nikol’skii – Besov class
M-term approximation
Acknowledgments: 
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan (project No. AP19677486). The author is grateful to the Reviewer for his comments.
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Received: 
24.02.2024
Accepted: 
16.07.2024
Published: 
30.05.2025
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