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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 8, Pages 1233–1240
DOI: https://doi.org/10.7868/S0044466913080024 (Mi zvmmf9896) 		 
Convergence rate estimates for “spherical” partial sums of double Fourier series

V. A. Abilova, M. V. Abilovb, M. K. Kerimovc

a Daghestan State University
b Daghestan State Technical University
c Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.7868/S0044466913080024
Abstract: The convergence of Fourier double series of $2\pi$-periodic functions from the space $\mathbb{L}_2$ is analyzed. The convergence rate of spherical partial sums of a double Fourier series is estimated for some classes of functions characterized by a generalized modulus of continuity.
Key words: Steklov function, shift operator, generalized modulus of continuity, spherical partial sums of double Fourier series in $\mathbb{L}_2$.
Received: 25.03.2013
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 8, Pages 1062–1069
DOI: https://doi.org/10.1134/S0965542513080022
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: V. A. Abilov, M. V. Abilov, M. K. Kerimov, “Convergence rate estimates for “spherical” partial sums of double Fourier series”, Zh. Vychisl. Mat. Mat. Fiz., 53:8 (2013), 1233–1240; Comput. Math. Math. Phys., 53:8 (2013), 1062–1069
Citation in format AMSBIB
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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