Geodesic
On Steklov's conjecture in the theory of orthogonal polynomials
Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 549-575 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper constructs an example of a weight function $\rho(x)$ on the interval $[-1, 1]$, such that $\rho(x)\geqslant\delta > 0$, $x\in[-1, 1]$, whereas the corresponding sequence of orthonormal polynomials is unbounded at $0$. Bibliography: 6 titles. 
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     author = {E. A. Rakhmanov},
     title = {On {Steklov's} conjecture in the theory of orthogonal polynomials},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_4_a6/}
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E. A. Rakhmanov. On Steklov's conjecture in the theory of orthogonal polynomials. Sbornik. Mathematics, Tome 36 (1980) no. 4, pp. 549-575. http://geodesic.mathdoc.fr/item/SM_1980_36_4_a6/

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

[2] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962

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

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

[5] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, izd-vo “Nauka”, Moskva, 1973 | MR

[6] E. A. Rakhmanov, “Ob asimptotike otnosheniya ortogonalnykh mnogochlenov”, Matem. sb., 103(145) (1977), 237–252 | Zbl