Szego polynomials: a view from the Riemann-Hilbert window

2005/08/06 by A. Martinez-Finkelshtein, Martinez-Finkelshtein, A.
Mathematics · #42C05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:42C05

paper · pdf · doi:10.48550/arxiv.math/0508117

23 pages, 7 figures; To appear in Elect. Trans. Num. Anal. Apparently, due to some missing .sty file, all integrals in version 2 were gone. Version 3 is a mere correction of this problem

arxiv created 2006/01/03 · arxiv updated 2009/12/01

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.

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