Geodesic
Polynomials, orthogonal on non-uniform grids
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 29-42 
A. A. Nurmagomedov. Polynomials, orthogonal on non-uniform grids. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 3, pp. 29-42. http://geodesic.mathdoc.fr/item/ISU_2011_11_3_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Agakhanov S. A., Natanson G. I., “Funktsiya Lebega summ Fure–Yakobi”, Vestn. Leningr. un-ta, 1968, no. 1, 11–13

[2] Badkov V. M., “Otsenki funktsii Lebega i ostatka ryada Fure–Yakobi”, Sib. mat. zhurn., 9:6 (1968), 1263–1283 | MR | Zbl

[3] Sharapudinov I. I., “O skhodimosti metoda naimenshikh kvadratov”, Mat. zametki, 53:3 (1993), 131–143 | MR | Zbl

[4] Daugavet I. K., Rafalson C. Z., “O nekotorykh neravenstvakh dlya algebraicheskikh mnogochlenov”, Vestn. Leningrad. un-ta, 1974, no. 19, 18–24 | MR | Zbl

[5] Konyagin C. V., “O neravenstve V. A. Markova dlya mnogochlenov v metrike $L$”, Tr. Mat. in-ta AN SSSR, 145, 1980, 117–125 | MR | Zbl

[6] Nurmagomedov A. A., “Ob asimptotike mnogochlenov, ortogonalnykh na proizvolnykh setkakh”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 8:1 (2008), 28–31

[7] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962