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Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle

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URI: https://hdl.handle.net/10016/6366
ISSN: 0021-9045
DOI: 10.1006/jath.1997.3126
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ratio_lagomasino_jat_1998_ps.pdf (535.84 KB)
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1998-02
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Elsevier
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Abstract
Ratio and relative asymptotics are given for sequences of polynomials orthogonal with respect to measures supported on an arc of the unit circle, where their absolutely continuous component is positive almost everywhere. The results obtained extend to this setting known ones given by Rakhmanov and Máté, Nevai, and Totik for the case when the arc is the whole unit circle. Technically speaking, the main feature is the use of orthogonality with respect to varying measures.
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29 pages, no figures.-- MSC2000 codes: 42C05, 30E10, 30E15.
MR#: MR1604927 (99c:42041)
Zbl#: Zbl 0897.42016
Keywords
Orthogonal polynomials, Ratio asymptotics, Logarithmic capacity
Bibliographic citation
Journal of Approximation Theory, 1998, vol. 92, n. 2, p. 216-244
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