Asymptotic behaviour of Verblunsky coefficients
- Alfaro, M.P. 1
- Hernández, M.B. 2
- Montaner, J.M. 1
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1
Universidad de Zaragoza
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2
Universidad de La Rioja
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ISSN: 0022-247X
Année de publication: 2006
Volumen: 324
Número: 2
Pages: 1050-1061
Type: Article
beta Ver similares en nube de resultadosD'autres publications dans: Journal of Mathematical Analysis and Applications
Résumé
Let V (z) = ∏ j = 1 m (z - ζ j), ζ h ≠ ζ k, h ≠ k and | ζ j | = 1, j = 1, ..., m, and consider the polynomials orthogonal with respect to | V | 2 d μ, φ n (| V | 2 d μ ; z), where μ is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szego{combining double acute accent} function has an analytic extension beyond | z | < 1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained. © 2006 Elsevier Inc. All rights reserved.