Critical points of orthogonal polynomials

  1. Alfaro, M.P. 1
  2. Bello-Hernández, M. 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: 2017

Volumen: 455

Número: 2

Páginas: 1655-1667

Tipo: Artículo

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DOI: 10.1016/J.JMAA.2017.06.060 SCOPUS: 2-s2.0-85021365057 WoS: WOS:000406568800044 GOOGLE SCHOLAR

Otras publicaciones en: Journal of Mathematical Analysis and Applications

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Resumen

We study properties of the critical points of orthogonal polynomials with respect to a measure on the unit circle (OPUC). The main result states that, under some conditions, the asymptotic distribution of the critical points of OPUC coincides with the asymptotic distribution of its zeros and each Nevai–Totik point attracts the same number of critical points as zeros of the OPUC. Analogous results are also presented for paraorthogonal polynomials and for orthogonal polynomials with respect to a regular measure supported on a continuum set. © 2017 Elsevier Inc.