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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 8, Pages 1364–1368 (Mi zvmmf4731)  
This article is cited in 6 scientific papers (total in 6 papers)

Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$

V. A. Abilova, M. K. Kerimovb

a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia
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Abstract: Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov $N$-widths of these classes. These results find applications in numerical analysis.
Key words: orthogonal polynomials, double Fourier series, generalized modulus of continuity, Kolmogorov $N$-width, convergence rate estimate for double Fourier series.
Received: 03.02.2009
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 8, Pages 1298–1302
DOI: https://doi.org/10.1134/S0965542509080028
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: V. A. Abilov, M. K. Kerimov, “Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$”, Zh. Vychisl. Mat. Mat. Fiz., 49:8 (2009), 1364–1368; Comput. Math. Math. Phys., 49:8 (2009), 1298–1302
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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