The Asymptotic Behavior of Carleman Orthogonal Polynomials
13th International Conference in Approximation Theory, Frontiers in Orthogonal Polynomials Mini-symposium
San Antonio, TX, USA
Let L be an analytic Jordan curve in the complex plane C. Polynomials that are orthonormal with respect to area measure over the interior domain of L were first considered by Carleman, who established a strong asymptotic formula for the polynomials valid on certain open neighborhood of the closed exterior of L. Here we extend the validity of Carleman’s asymptotic formula to a maximal open set, every boundary point of which is an accumulation point of the zeros of the polynomials.
Orthogonal polynomials, Carleman's theorem
Analysis | Mathematics
Peter D. Dragnev (2010).
The Asymptotic Behavior of Carleman Orthogonal Polynomials. Presented at 13th International Conference in Approximation Theory, Frontiers in Orthogonal Polynomials Mini-symposium, San Antonio, TX, USA.