Asymptotic behaviour of Verblunsky coefficients

  1. Alfaro, M.P. 1
  2. Hernández, M.B. 2
  3. Montaner, J.M. 1
  1. 1 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Año de publicación: 2006

Volumen: 324

Número: 2

Páginas: 1050-1061

Tipo: Artículo

DOI: 10.1016/J.JMAA.2006.01.015 SCOPUS: 2-s2.0-33749566583 WoS: WOS:000241752600024 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

Repositorio institucional: lock_openAcceso abierto Editor lock_openAcceso abierto Postprint

Resumen

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.