Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight
Abstract
We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight e-nV( x), assuming that the potential V has four bounded derivatives on [-1,1] and the equilibrium measure has a one interval support. We obtain the asymptotics as a solution of the system of "string" equations.
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