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Please use this identifier to cite or link to this item:
http://hdl.handle.net/10016/5901
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| Title: | Szegö transformations and Nth order associated polynomials on the unit circle |
| Author(s): | Garza, Luis
Marcellán, Francisco |
| Publisher: | Elsevier |
| Issued date: | May-2009 |
| Citation: | Computers and Mathematics with Applications, 2009, vol. 57, n. 10, p. 1659-1671 |
| URI: | http://hdl.handle.net/10016/5901 |
| ISSN: | 0898-1221 |
| DOI: | 10.1016/j.camwa.2009.03.040 |
| Description: | 13 pages, no figures.-- MSC2000 codes: 42C05, 15A23. |
| Abstract: | In this paper we analyze the Stieltjes functions defined by the Szegö inverse transformation of a nontrivial probability measure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their Verblunsky parameters. Such polynomials are called anti-associated (respectively associated) orthogonal polynomials. Thus, rational spectral transformations appear in a natural way. |
| Sponsor: | The work of the first author has been supported by a grant of Universidad Autónoma de Tamaulipas. The work of the second author has been supported by Dirección General de Investigación, Ministerio de Educación y Ciencia of Spain, grant MTM06-13000-C03-02. Both authors have been supported by project CCG07-UC3M/ESP-3339 with the financial support of Comunidad de Madrid-Universidad Carlos III de Madrid. |
| Review: | PeerReviewed |
| Publisher version: | http://dx.doi.org/10.1016/j.camwa.2009.03.040 |
| Keywords: | Probability measures
Szegö transformations
Orthogonal polynomials
Nth associated orthogonal polynomials
Verblunsky parameters
Rational spectral transformations
Carathéodory and Stieltjes functions |
| Rights: | © Elsevier |
| Appears in Collections: | DM - GAMA - Artículos de Revistas
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