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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5915
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| Title: | Coherent pairs of linear functionals on the unit circle |
| Author(s): | Branquinho, A.
Foulquié, A.
Marcellán, Francisco
Rebocho, M. N. |
| Publisher: | Elsevier |
| Issued date: | Jul-2008 |
| Citation: | Journal of Approximation Theory, 2008, vol. 153, n. 1, p. 122-137 |
| URI: | http://hdl.handle.net/10016/5915 |
| ISSN: | 0021-9045 |
| DOI: | 10.1016/j.jat.2008.03.003 |
| Description: | 16 pages, no figures.-- 2000 MSC code: Primary 42C05.
MR#: MR2432558 (2009e:42048)
Zbl#: Zbl 1149.42013 |
| 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. |
| Sponsor: | The work of the first and fourth author was supported by (CMUC) Department of Mathematics, University of Coimbra. The second author would like to thank Unidade de investigação (Matemática e Aplicações) da Universidade de Aveiro. The work of the third author was supported by Dirección General de Investigación (Ministerio de Educación y Ciencia) of Spain under Grant MTM 2006-13000-C03-02. The work of M.N. Rebocho was supported by FCT, Fundação para a Ciência e Tecnologia, with Grant ref. SFRH/BD/25426/2005. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1016/j.jat.2008.03.003 |
| Keywords: | Orthogonal polynomials
Differential equations
Three-term recurrence relations
Measures on the unit circle
Hermitian functionals |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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