Critical points of orthogonal polynomials
- Alfaro, M.P. 1
- Bello-Hernández, M. 2
- Montaner, J.M. 1
-
1
Universidad de Zaragoza
info
-
2
Universidad de La Rioja
info
ISSN: 0022-247X
Year of publication: 2017
Volume: 455
Issue: 2
Pages: 1655-1667
Type: Article
More publications in: Journal of Mathematical Analysis and Applications
Abstract
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.