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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 7, Pages 1109–1117
DOI: https://doi.org/10.7868/S0044466915070029 (Mi zvmmf10230) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials

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

a Dagestan State University, ul. M. Gadzhieva 43a, Makhachkala, 367025, Russia
b Dagestan State Technical University, pr. Shamilya 70, Makhachkala, 367015, Russia
c Dorodnicyn Computing Center, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
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DOI: https://doi.org/10.7868/S0044466915070029
Abstract: Sharp estimates are obtained for the convergence rate of “triangular” and “hyperbolic” partial sums of Fourier series in orthogonal (Laguerre, Hermite, Jacobi) polynomials in the classes of differentiable functions of two variables characterized by a generalized modulus of continuity. The proofs are based on the generalized shift operator and generalized modulus of continuity for functions from $\mathbb{L}_2$ having generalized partial derivatives in Levi’s sense.
Key words: double Fourier series in orthogonal polynomials, “triangular” and “hyperbolic” partial sums, sharp estimates for the convergence rate of Fourier series, functions having generalized partial derivatives, generalized modulus of continuity, generalized shift operator.
Received: 25.02.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 7, Pages 1094–1102
DOI: https://doi.org/10.1134/S0965542515070027
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: V. A. Abilov, M. V. Abilov, M. K. Kerimov, “Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1109–1117; Comput. Math. Math. Phys., 55:7 (2015), 1094–1102
Citation in format AMSBIB
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