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

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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, Volume 11, Issue 3(2), Pages 29–42
DOI: https://doi.org/10.18500/1816-9791-2011-11-3-2-29-42 (Mi isu245)

This article is cited in 6 scientific papers (total in 6 papers)

Mathematics

Polynomials, orthogonal on non-uniform grids

A. A. Nurmagomedov

Dagestan State Pedagogical University, Makhachkala, Chair of Applied Mathematics

Full-text PDF (223 kB) Citations (6)

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

Abstract: Asymptotic properties of polynomials

{\hat{p}}_{n} (t)

$\hat p_n(t)$ , orthogonal with weight

Δ t_{j}

$\Delta t_j$ on any finite set of

N

$N$ points from segment

[- 1, 1]

$[-1,1]$ are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as

n

$n$ tends to infinity together with

N

$N$ 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.

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

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}

Linking options:

https://www.mathnet.ru/eng/isu245

https://www.mathnet.ru/eng/isu/v11/i4/p29

This publication is cited in the following 6 articles:

Z. M. Magomedova, A. A. Nurmagomedov, “Asimptoticheskie svoistva mnogochlenov $\hat{l}_{n,n}^\alpha(x)$ , ortogonalnykh na proizvolnykh setkakh”, Vladikavk. matem. zhurn., 24:2 (2022), 101–116
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
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
A. A. Nurmagomedov, “Approksimativnye svoistva diskretnykh summ Fure po mnogochlenam, ortogonalnym na neravnomernykh setkakh”, Vladikavk. matem. zhurn., 22:2 (2020), 34–47
Sultanakhmedov M.S., “on the Convergence of the Least Square Method in Case of Non-Uniform Grids”, Probl. Anal., 8:3 (2019), 166–186
A. A. Nurmagomedov, N. K. Rasulov, “Two-Sided Estimates of Fourier Sums Lebesgue Functions with Respect to Polynomials Orthogonal on Nonuniform Grids”, Vestnik St.Petersb. Univ.Math., 51:3 (2018), 249

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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