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A Cubic decomposition of sequences of orthogonal polynomials on the unit circle

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URI: https://hdl.handle.net/10016/6012
ISSN: 1747-6933
DOI: 10.1080/02781070290032252
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cubic_marcellan_cv_2002_ps.pdf (345.87 KB)
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2002-09
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Taylor & Francis
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Abstract
In this paper we will discuss the problem of generation of sequences of orthogonal polynomials with respect to measures supported on the unit circle from a given sequence of orthogonal polynomials using a perturbation of a cubic sieved process. The basic tools are the Szegö forward recurrence relation as well as the fact of the coprimality of orthogonal polynomials on the unit circle and their corresponding reverse polynomials. We also give the connection between the associated orthogonality measures. Finally, some examples of this cubic decomposition are shown.
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15 pages, no figures.-- MSC2000 codes: 42C05.
MR#: MR1925172 (2003g:42039)
Zbl#: Zbl 1026.42026
Keywords
Orthogonal polynomials, Reflection parameters, Carathéodory functions
Bibliographic citation
Complex Variables and Elliptic Equations, 2002, vol. 47, n. 9, p. 745-759
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