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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2025, Volume 65, Number 4, Pages 417–425
DOI: https://doi.org/10.31857/S0044466925040018 (Mi zvmmf11949) 		 
General numerical methods

Approximation of the function and its derivative relating to the Hölder–Lipschitz class with their Fourier coefficients for a harmonically modulated argument

N. D. Kuz'michev

Ogarev Mordovia State University, 430005, Saransk, Russia
DOI: https://doi.org/10.31857/S0044466925040018
Abstract: The paper considers the proved theorems according to which any function and its derivative relating to the Hölder–Lipschitz class $C^\alpha(G)$ can be approximated with any pre-set accuracy by a finite sum of the dependences of the Fourier coefficients for a harmonically modulated function argument.
Key words: Hölder–Lipschitz class, function, function derivative, harmonically modulated argument, approximation, Fourier coefficient dependencies.
Received: 05.10.2024
Revised: 03.12.2024
Accepted: 04.02.2025
English version:
Computational Mathematics and Mathematical Physics, 2025, Volume 65, Issue 4, Pages 663–673
DOI: https://doi.org/10.1134/S096554252570006X
Bibliographic databases:
Document Type: Article
UDC: 519.65; 517.521
Language: Russian
Citation: N. D. Kuz'michev, “Approximation of the function and its derivative relating to the Hölder–Lipschitz class with their Fourier coefficients for a harmonically modulated argument”, Zh. Vychisl. Mat. Mat. Fiz., 65:4 (2025), 417–425; Comput. Math. Math. Phys., 65:4 (2025), 663–673
Citation in format AMSBIB
\Bibitem{Kuz25}
\by N.~D.~Kuz'michev
\paper Approximation of the function and its derivative relating to the H\"older--Lipschitz class with their Fourier coefficients for a harmonically modulated argument
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2025
\vol 65
\issue 4
\pages 417--425
\mathnet{http://mi.mathnet.ru/zvmmf11949}
\elib{https://elibrary.ru/item.asp?id=82358149}
\transl
\jour Comput. Math. Math. Phys.
\yr 2025
\vol 65
\issue 4
\pages 663--673
\crossref{https://doi.org/10.1134/S096554252570006X}
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