Critical points of orthogonal polynomials
- Alfaro, M.P. 1
- Bello-Hernández, M. 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
Argitalpen urtea: 2017
Alea: 455
Zenbakia: 2
Orrialdeak: 1655-1667
Mota: Artikulua
Beste argitalpen batzuk: Journal of Mathematical Analysis and Applications
Laburpena
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.