Critical points of orthogonal polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Pilar Alfaro, Maria¹  Bello-Hernandez, Manuel²  Maria Montaner, Jesus³ 

[1] Univ Zaragoza, Dept Matemat, Calle Pedro Cerbuna S-N, E-50009 Zaragoza, Spain

[2] Univ La Rioja, Dept Matemat & Comp, Edif Cient Tecnol,Calle Madre de Dios 53, Logrono 26006, Spain

[3] Univ Zaragoza, Dept Matemat Aplicada, Edif Torres Quevedo,Calle Maria de Luna 3, Zaragoza 50018, Spain

关键词: Orthogonal polynomials;    Zeros;    Critical points;    Asymptotics;   

DOI  :  10.1016/j.jmaa.2017.06.060

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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