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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 9, Pages 1545–1565 (Mi zvmmf409)  

This article is cited in 3 scientific papers (total in 3 papers)

Some estimates for the error in mixed Fourier–Bessel expansions of functions of two variables

V. A. Abilova, M. K. Kerimovb

a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
b Dorodnitsyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: Some issues concerning expansions of functions of two variables in mixed Fourier–Bessel series are considered. In particular, the rate of their convergence in the classes of functions characterized by generalized moduli of continuity are estimated, and estimates of the remainder terms are obtained.

Key words: mixed Fourier–Bessel series, estimates of remainder terms, widths, absolute convergence conditions for Fourier series.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:9, 1465–1486

Bibliographic databases:

UDC: 519.651
Received: 14.04.2006

Citation: V. A. Abilov, M. K. Kerimov, “Some estimates for the error in mixed Fourier–Bessel expansions of functions of two variables”, Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1545–1565; Comput. Math. Math. Phys., 46:9 (2006), 1465–1486

Citation in format AMSBIB
\Bibitem{AbiKer06}
\by V.~A.~Abilov, M.~K.~Kerimov
\paper Some estimates for the error in mixed Fourier--Bessel expansions of functions of two variables
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 9
\pages 1545--1565
\mathnet{http://mi.mathnet.ru/zvmmf409}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287657}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 9
\pages 1465--1486
\crossref{https://doi.org/10.1134/S0965542506090028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749039945}


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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, G. A. Djalaeva, M. K. Kerimov, “On expansions of functions of two variables in mixed Fourier–Jacobi series and their application for estimation of errors of cubature formulas”, Comput. Math. Math. Phys., 47:8 (2007), 1243–1252  mathnet  crossref  mathscinet
    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. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “On sharp estimates of the convergence of double Fourier–Bessel series”, Comput. Math. Math. Phys., 57:11 (2017), 1735–1740  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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