Asymptotics of polynomials orthogonal over the unit disk with respect to a polynomial weight without zeros on the unit circle

作者：Mina Diaz Erwin^*

来源：Journal of Approximation Theory, 2013, 165(1): 41-59.

DOI：10.1016/j.jat.2012.09.006

• Orthogonal polynomials
• Asymptotic behavior
• Weighted Bergman kernel

We establish asymptotic formulas for polynomials that are orthogonal over the unit disk with respect to a weight of the form vertical bar omega(z)vertical bar(2), where omega(z) is a polynomial without zeros on the unit circle vertical bar z vertical bar = 1. The formulas put in evidence a strong connection between the behavior of the polynomials and the reproducing kernel of an associated weighted Bergman space, which produces interesting new features in the presence of a weight omega with interior zeros.

• 出版日期2013-1