Szegő orthogonal polynomials with respect to an analytic weight: canonical representation and strong asymptotics

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We provide a representation in terms of certain canonical functions for a sequence of polynomials orthogonal with respect to a weight that is strictly positive and analytic on the unit circle. These formulas yield a complete asymptotic expansion for these polynomials, valid uniformly in the whole complex plane. As a consequence, we obtain some results about the distribution of zeros of these polynomials. The main technique is the steepest descent analysis of Deift and Zhou, based on the matrix Riemann-Hilbert characterization proposed by Fokas, Its and Kitaev.
49 pages, 19 figures

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Classical Analysis and ODEs, Complex Variables, 42C05

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http://salesiana.dossiersoluciones.com/handle/123456789/74200

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0502300
 http://arxiv.org/abs/math/0502300

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arXiv