Title

The Asymptotic Behavior of Carleman Orthogonal Polynomials

Document Type

Presentation

Presentation Date

2010

Conference Name

13th International Conference in Approximation Theory, Frontiers in Orthogonal Polynomials Mini-symposium

Conference Location

San Antonio, TX, USA

Peer Review

Invited

Abstract

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.

Keywords

Orthogonal polynomials, Carleman's theorem

Disciplines

Analysis | Mathematics

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Link to Original Published Item

http://www.math.vanderbilt.edu/~at13/