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Zh. Vychisl. Mat. Mat. Fiz., 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:8, 1298–1302

Bibliographic databases:

UDC: 519.651
Received: 03.02.2009

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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\by V.~A.~Abilov, M.~K.~Kerimov
\paper Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space $L_2((a,b)\times(c,d);p(x)q(y)))$
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 8
\pages 1364--1368
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\zmath{https://zbmath.org/?q=an:05649680}
\transl
\jour Comput. Math. Math. Phys.
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\vol 49
\issue 8
\pages 1298--1302
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Sharp estimates for the rate of convergence of Fourier series of functions of a complex variable in the space $L\sb 2(D,p(z))$”, Comput. Math. Math. Phys., 50:6 (2010), 946–950  mathnet  crossref  mathscinet  adsnasa  isi  elib
    2. V. A. Abilov, M. K. Kerimov, “Sharp estimates for the convergence rate of “hyperbolic” partial sums of double fourier series in orthogonal polynomials”, Comput. Math. Math. Phys., 52:11 (2012), 1497–1503  mathnet  crossref  mathscinet  isi  elib  elib
    3. Brive B., Finet C., Tkebuchava G.E., “A generalization of the Riesz-Fischer theorem and linear summability methods”, J. Approx. Theory, 164:6 (2012), 841–853  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. D. Chernyshov, “Method of fast expansions for solving nonlinear differential equations”, Comput. Math. Math. Phys., 54:1 (2014), 11–21  mathnet  crossref  crossref  isi  elib  elib
    5. V. A. Abilov, M. V. Abilov, M. K. Kerimov, “Sharp estimates for the rate of convergence of double Fourier series in classical orthogonal polynomials”, Comput. Math. Math. Phys., 55:7 (2015), 1094–1102  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. F. V. Abilova, E. V. Selimkhanov, “Sharp estimates for the convergence rate of Fourier series in two variables and their applications”, Comput. Math. Math. Phys., 58:10 (2018), 1545–1551  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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