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Coherent pairs of linear functionals on the unit circle

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URI: https://hdl.handle.net/10016/5915
ISSN: 0021-9045
DOI: 10.1016/j.jat.2008.03.003
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coherent_marcellan_jat_2008_ps.pdf (625.45 KB)
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2008-07
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Elsevier
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Abstract
In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if (μ0,μ1) is a coherent pair of measures on the unit circle, then μ0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with μ1 is a specific rational transformation of the linear functional corresponding to μ0. Some examples are given.
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16 pages, no figures.-- 2000 MSC code: Primary 42C05.
MR#: MR2432558 (2009e:42048)
Zbl#: Zbl 1149.42013
Keywords
Orthogonal polynomials, Differential equations, Three-term recurrence relations, Measures on the unit circle, Hermitian functionals
Bibliographic citation
Journal of Approximation Theory, 2008, vol. 153, n. 1, p. 122-137
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