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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

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

This article is cited in 6 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.

UDC: 517.5

DOI: 10.18500/1816-9791-2011-11-3-2-29-42



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