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

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dc.creatorMartinez-Finkelshtein, A.
dc.creatorMcLaughlin, K. T. -R.
dc.creatorSaff, E. B.
dc.date2005-02-15
dc.date.accessioned2026-07-07T05:17:01Z
dc.date.available2026-07-07T05:17:01Z
dc.descriptionWe 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.
dc.description49 pages, 19 figures
dc.identifierhttps://arxiv.org/abs/math/0502300
dc.identifierhttp://arxiv.org/abs/math/0502300
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74200
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject42C05
dc.titleSzegő orthogonal polynomials with respect to an analytic weight: canonical representation and strong asymptotics
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