Geodesic
Estimates of the growth of orthogonal polynomials whose weight is bounded away from zero
Sbornik. Mathematics, Tome 42 (1982) no. 2, pp. 237-263 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that for any $\varepsilon>0$ and any point $x_0$ in the interval $(-1,1)$ there exists a weight function $\rho(x)$ on $[-1,1]$ with $\rho(x)\geqslant1$, $x\in[-1,1]$, such that the following inequalities hold for the corresponding orthonormal polynomials $p_n(x)$: $$ |p_n(x_0)|\geqslant n^{1/2-\varepsilon},\qquad n\in\Lambda, $$ where $\Lambda$ is some infinite sequence of positive integers. Bibliography: 7 titles. 
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E. A. Rakhmanov. Estimates of the growth of orthogonal polynomials whose weight is bounded away from zero. Sbornik. Mathematics, Tome 42 (1982) no. 2, pp. 237-263. http://geodesic.mathdoc.fr/item/SM_1982_42_2_a2/

[1] Steklov V. A., “Une methode de la solution du probleme de development des fonctions en series de polynomes de Tchebysheff independante de la theorie de fermeture”, Izv. Ros. AN, 1921, 281–302, 303–326

[2] Suetin P. K., “Problema V. A. Steklova v teorii ortogonalnykh mnogochlenov”, Itogi nauki i tekhniki. Matem. analiz, 15, VINITI, M., 1977, 5–82 | MR

[3] Rakhmanov E. A., “O gipoteze Steklova v teorii ortogonalnykh mnogochlenov”, Matem. sb., 108(150) (1979), 581–608 | MR | Zbl

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

[5] Geronimus Ya. L., Mnogochleny, ortogonalnye na okruzhnosti i otrezke, Fizmatgiz, M., 1958 | Zbl

[6] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR

[7] Rakhmanov E. A., “K probleme V. A. Steklova v teorii ortogonalnykh mnogochlenov”, DAN SSSR, 254:4 (1980) | MR | Zbl