Szego polynomials: a view from the Riemann-Hilbert window
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2006Resumen
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.
Palabra/s clave
Ceros
Asintóticas
Problemas de Riemann-Hilbert
Polinomios de Szego
Coeficientes de Verblunsky
Zeros
Asymptotics
Riemann-Hilbert problem
Szego polynomials
Verblunsky coefficients