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Izv. Saratov Univ. Math. Mech. Inform., 2011, Volume 11, Issue 3(2), Pages 29–42 (Mi isu245)  

This article is cited in 4 scientific papers (total in 4 papers)

Mathematics

Polynomials, orthogonal on non-uniform grids

A. A. Nurmagomedov

Dagestan State Pedagogical University, Makhachkala, Chair of Applied Mathematics

Abstract: Asymptotic properties of polynomials $\hat p_n(t)$, orthogonal with weight $\Delta t_j$ on any finite set of $N$ points from segment $[-1,1]$ are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as $n$ tends to infinity together with $N$ is closely related to asymptotic behaviour of the Lasiandra polynomials. Furthermore are investigated the approximating properties of the sums by Fourier on these polynomials.

Key words: polinomial, ortogonal system, set, weight, weighted estimate, asymptotic formula, approximation.

DOI: https://doi.org/10.18500/1816-9791-2011-11-3-2-29-42

Full text: PDF file (223 kB)
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UDC: 517.5

Citation: A. A. Nurmagomedov, “Polynomials, orthogonal on non-uniform grids”, Izv. Saratov Univ. Math. Mech. Inform., 11:3(2) (2011), 29–42

Citation in format AMSBIB
\Bibitem{Nur11}
\by A.~A.~Nurmagomedov
\paper Polynomials, orthogonal on non-uniform grids
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2011
\vol 11
\issue 3(2)
\pages 29--42
\mathnet{http://mi.mathnet.ru/isu245}
\crossref{https://doi.org/10.18500/1816-9791-2011-11-3-2-29-42}
\elib{https://elibrary.ru/item.asp?id=16816036}


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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. Sultanakhmedov M.S., “on the Convergence of the Least Square Method in Case of Non-Uniform Grids”, Probl. Anal., 8:3 (2019), 166–186  crossref  mathscinet  zmath  isi  scopus
    2. A. A. Nurmagomedov, “The approximation of functions by partial sums of the Fourier series in polynomials orthogonal on arbitrary grids”, Russian Math. (Iz. VUZ), 64:4 (2020), 54–63  mathnet  crossref  crossref  isi
    3. A. A. Nurmagomedov, “Approksimativnye svoistva diskretnykh summ Fure po mnogochlenam, ortogonalnym na neravnomernykh setkakh”, Vladikavk. matem. zhurn., 22:2 (2020), 34–47  mathnet  crossref
    4. M. S. Sultanakhmedov, “Approximation of Functions by Discrete Fourier Sums in Polynomials Orthogonal on a Nonuniform Grid with Jacobi Weight”, Math. Notes, 110:3 (2021), 418–431  mathnet  crossref  crossref  isi
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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