Abstract.
Ratio asymptotics for orthogonal polynomials on the unit circle is characterized in terms of the existence of lim n |Φ n (0)| and {lim n [ Φ n+1 (0)/ Φ n (0)] , where \( \{\Phi_n(0)\}_{n \geq 0} \) denotes the sequence of reflection coefficients. The limit periodic case, that is, when these limits exist for n = j mod k , j = 1, . . ., k , is also considered.
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December 27, 1996. Date revised: October 14, 1997. Date accepted: December 22, 1997.
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Barrios Rolanía, D., López Lagomasino, G. Ratio Asymptotics for Polynomials Orthogonal on Arcs of the Unit Circle. Constr. Approx. 15, 1–31 (1999). https://doi.org/10.1007/s003659900095
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DOI: https://doi.org/10.1007/s003659900095