Publication:
Ratio asymptotics for polynomials orthogonal on arcs of the unit circle

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ISSN: 0176-4276 (Print)
ISSN: 1432-0940 (Online)
Publication date
1999-09
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Springer
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Abstract
Ratio 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.
Description
30 pages, no figures.-- MSC1991 code: Primary 42C05.
MR#: MR1660089 (99j:42033)
Zbl#: Zbl 0931.42016
Keywords
Orthogonal polynomials, Ratio asymptotics, Reflection coefficients
Bibliographic citation
Constructive Approximation, 1999, vol. 15, n. 1, p. 1-31