Geodesic
On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szeg\"o's condition
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 149-167

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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. 
@article{SM_1987_58_1_a8,
     author = {E. A. Rakhmanov},
     title = {On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the {Szeg\"o's} condition},
     journal = {Sbornik. Mathematics},
     pages = {149--167},
     publisher = {mathdoc},
     volume = {58},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_1_a8/}
}
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E. A. Rakhmanov. On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szeg\"o's condition. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 149-167. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a8/