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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 11, Pages 1765–1770
DOI: https://doi.org/10.7868/S0044466917110023 (Mi zvmmf10632) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On sharp estimates of the convergence of double Fourier–Bessel series

V. A. Abilova, F. V. Abilovaa, M. K. Kerimovb

a Dagestan State Technical University, Makhachkala, Dagestan, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (118 kB) Citations (1) English version article
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DOI: https://doi.org/10.7868/S0044466917110023
Abstract: The problem of approximation of a differentiable function of two variables by partial sums of a double Fourier-Bessel series is considered. Sharp estimates of the rate of convergence of the double Fourier–Bessel series on the class of differentiable functions of two variables characterized by a generalized modulus of continuity are obtained. The proofs of four theorems on this issue, which can be directly applied to solving particular problems of mathematical physics, approximation theory, etc., are presented.
Key words: double Fourier–Bessel series, best approximation, spherical partial sums, generalized shift operator, generalized modulus of continuity.
Received: 22.05.2017
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 11, Pages 1735–1740
DOI: https://doi.org/10.1134/S0965542517110021
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: V. A. Abilov, F. V. Abilova, M. K. Kerimov, “On sharp estimates of the convergence of double Fourier–Bessel series”, Zh. Vychisl. Mat. Mat. Fiz., 57:11 (2017), 1765–1770; Comput. Math. Math. Phys., 57:11 (2017), 1735–1740
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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