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arXiv:1006.5515 [math-ph]AbstractReferencesReviewsResources

Asymptotic behavior of the Verblunsky coefficients for the OPUC with a varying weight

Poplavskyi Mihail

Published 2010-06-29, updated 2013-06-28Version 2

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.

Comments: 28 pages
Journal: J. Math. Phys. 53, 043510 (2012)
Categories: math-ph, math.MP
Subjects: 15B52, 33C47, 02.10.De
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