Abstract
Consider a system {φ n } of polynomials orthonormal on the unit circle with respect to a measuredμ, withμ′>0 almost everywhere. Denoting byk n the leading coefficient ofφ n , a simple new proof is given for E. A. Rakhmanov's important result that lim n→∞,k n /k n+1=1; this result plays a crucial role in extending Szegö's theory about polynomials orthogonal with respect to measuresdμ with logμ′∈L 1 to a wider class of orthogonal polynomials.
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Communicated by Edward B. Saff.
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Máté, A., Nevai, P. & Totik, V. Asymptotics for the ratio of leading coefficients of orthonormal polynomials on the unit circle. Constr. Approx 1, 63–69 (1985). https://doi.org/10.1007/BF01890022
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DOI: https://doi.org/10.1007/BF01890022