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

Zeitschrift:
Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

Datum der Publikation: 2017

Ausgabe: 455

Nummer: 2

Seiten: 1655-1667

Art: Artikel

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

Andere Publikationen in: Journal of Mathematical Analysis and Applications

Institutionelles Repository: lock_openOpen Access Editor lock_openOpen Access Postprint

Zusammenfassung

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.