Geodesic
On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szegö's condition
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 149-167 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author considers asymptotic properties of polynomials $\varphi_n(z)$, orthonormal on the unit circle $\Gamma$, with weights $f(z)$ that do not satisfy Szegö's condition. It is shown, in particular, that if $f(z)$ satisfies a Dini–Lipschitz condition, then $\lim_{n\to\infty}|\varphi_n(z)|=f(z)^{-1/2}$ uniformly on each set $\gamma\subset\Gamma$ on which $f$ has a positive lower bound. Bibliography: 9 titles. 
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     title = {On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the {Szeg\"o's} condition},
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     year = {1987},
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E. A. Rakhmanov. On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szegö's condition. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 149-167. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a8/

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