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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 6, Pages 966–980 (Mi zvmmf4700)  
This article is cited in 14 scientific papers (total in 14 papers)

Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$

V. A. Abilova, F. V. Abilovab, M. K. Kerimovc

a Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
b Dagestan State Technical University, pr. Kalinina 70, Makhachkala, 367015, Russia
c Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
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Abstract: Sharp estimates are given for the convergence rate of Fourier series in terms of classical orthogonal polynomials in some classes of functions characterized by a generalized modulus of continuity in the space $L_2((a,b),p(x))$. Expansions in terms of Laguerre, Hermite, and Jacobi polynomials are considered.
Key words: Fourier series, generalized modulus of continuity, width, generalized derivatives, expansions in terms of Laguerre, Hermite, Jacobi polynomials, convergence of series.
Received: 05.12.2008
Revised: 28.12.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 6, Pages 927–941
DOI: https://doi.org/10.1134/S0965542509060049
Bibliographic databases:
Document Type: Article
UDC: 519.651
Language: Russian
Citation: V. A. Abilov, F. V. Abilova, M. K. Kerimov, “Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$”, Zh. Vychisl. Mat. Mat. Fiz., 49:6 (2009), 966–980; Comput. Math. Math. Phys., 49:6 (2009), 927–941
Citation in format AMSBIB
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\paper Sharp estimates for the convergence rate of Fourier series in terms of orthogonal polynomials in $L_2((a,b),p(x))$
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 6
\pages 966--980
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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