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Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight (1006.5515v2)
Published 29 Jun 2010 in math-ph and math.MP
Abstract: We present an asymptotic analysis of the Verblunsky coefficients for the polynomials orthogonal on the unit circle with the varying weight $e{-nV(\cos x)}$, 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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