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30 pages, no figures.-- MSC1991 code: Primary 42C05.MR#: MR1660089 (99j:42033)Zbl#: Zbl 0931.42016Ratio asymptotics for orthogonal polynomials on the unit circle is characterized in terms of the existence of $\lim_n  Phi_n(0)  and $\lim_n {\Phi_{n+1}(0) \over \Phi_{n}(0)}$, where $\{\Phi_n(z)\}_{n\geq 0}$ 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.The research of G. López Lagomasino was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and byINTAS under grant 93-0219 EXT.Publicad

Ratio Asymptotics for Polynomials Orthogonal on Arcs of the Unit Circle