Asymptotics for polynomials orthogonal over the unit disk with respect to a positive polynomial weight |
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Authors: | Erwin Miña-Díaz |
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Institution: | University of Mississippi, Department of Mathematics, Hume Hall 305, P.O. Box 1848, University, MS 38677-1848, USA |
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Abstract: | We derive asymptotics for polynomials orthogonal over the complex unit disk with respect to a weight of the form 2|h(z)|, with h(z) a polynomial without zeros in |z|<1. The behavior of the polynomials is established at every point of the complex plane. The proofs are based on adapting to the unit disk a technique of J. Szabados for the asymptotic analysis of polynomials orthogonal over the unit circle with respect to the same type of weight. |
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Keywords: | Orthogonal polynomials Asymptotic behavior |
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