Geodesic
On the possible rate of growth of polynomials orthogonal with a continuous positive weight
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 311-331 
M. U. Ambroladze. On the possible rate of growth of polynomials orthogonal with a continuous positive weight. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 311-331. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that there are continuous positive weights such that the orthogonal polynomials constructed with respect to them are not uniformly bounded at a given point, both for the circle and for a closed interval. Furthermore, in the case of the circle the orthogonal polynomials have logarithmic growth. Also determined is a minimal (in a certain sense) class of positive continuous functions in which there exists a weight function having the property indicated.

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