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Sibirsk. Mat. Zh., 2017, Volume 58, Number 2, Pages 440–467 (Mi smj2872)  

This article is cited in 5 scientific papers (total in 5 papers)

Special series in Laguerre polynomials and their approximation properties

I. I. Sharapudinovab

a Southern Mathematical Institute, Vladikavkaz, Russia
b Dagestan State Pedagogical University, Makhachkala, Russia

Abstract: We consider special series in the classical Laguerre polynomials coinciding in particular cases with the mixed series associated to Laguerre polynomials, introduced by the author previously, as well as Fourier–Sobolev series in Sobolev orthogonal Laguerre polynomials. We address the questions of uniform convergence of these series on a finite segment of the positive half-axis. We study the approximation properties of partial sums of special series on the positive half-axis, with particular attention paid to estimating their Lebesgue function.

Keywords: Sobolev orthogonal Laguerre polynomials, mixed series, special series in Laguerre polynomials, approximation properties.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00486-а
The author was supported by the Russian Foundation for Basic Research (Grant 16-01-00486-a).


DOI: https://doi.org/10.17377/smzh.2017.58.217

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English version:
Siberian Mathematical Journal, 2017, 58:2, 338–362

Bibliographic databases:

UDC: 517.538
MSC: 35R30
Received: 18.09.2015

Citation: I. I. Sharapudinov, “Special series in Laguerre polynomials and their approximation properties”, Sibirsk. Mat. Zh., 58:2 (2017), 440–467; Siberian Math. J., 58:2 (2017), 338–362

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. I. Sharapudinov, “Obraschenie preobrazovaniya Laplasa posredstvom obobschennykh spetsialnykh ryadov po polinomam Lagerra”, Dagestanskie elektronnye matematicheskie izvestiya, 2017, no. 8, 7–20  mathnet  crossref
    2. R. M. Gadzhimirzaev, “Approximative properties of Fourier–Meixner sums”, Probl. anal. Issues Anal., 7(25):1 (2018), 23–40  mathnet  crossref  elib
    3. I. I. Sharapudinov, “Sobolev orthogonal polynomials associated with Chebyshev polynomials of the first kind and the Cauchy problem for ordinary differential equations”, Differ. Equ., 54:12 (2018), 1602–1619  crossref  mathscinet  zmath  isi  scopus
    4. I. I. Sharapudinov, M. G. Magomed-Kasumov, “On representation of a solution to the Cauchy problem by a Fourier series in Sobolev-orthogonal polynomials generated by Laguerre polynomials”, Differ. Equ., 54:1 (2018), 49–66  crossref  mathscinet  zmath  isi  scopus
    5. M. G. Magomed-Kasumov, “Sistema funktsii, ortogonalnaya v smysle Soboleva i porozhdennaya sistemoi Uolsha”, Matem. zametki, 105:4 (2019), 545–552  mathnet  crossref  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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