Asymptotic behavior of the CMV matrix coefficients for the OPUC with a varying weight

Details Asymptotic behavior of the CMV matrix coefficients for the OPUC with a varying weight Asymptotic behavior of the CMV matrix coefficients for the OPUC with a varying weight

2010-06-29

arxiv.org/abs/1006.5515v1

Physics

Mathematical Physics

24 pages

Scientific paper

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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