Volume 25, pp. 369-392, 2006.

Szegő polynomials: a view from the Riemann-Hilbert window

A. Martínez-Finkelshtein

Abstract

This is an expanded version of the talk given at the conference “Constructive Functions Tech-04”. We survey some recent results on canonical representation and asymptotic behavior of polynomials orthogonal on the unit circle with respect to an analytic weight. These results are obtained using the steepest descent method based on the Riemann-Hilbert characterization of these polynomials.

Full Text (PDF) [597 KB]

Key words

zeros, asymptotics, Riemann-Hilbert problem, Szegő polynomials, Verblunsky coefficients

AMS subject classifications

33C45

Links to the cited ETNA articles

[16]Vol. 25 (2006), pp. 328-368 Barry Simon: Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures

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