Sharp lower bounds for the Widom factors on the real line

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Alpan, Gokalp¹  Zinchenko, Maxim² 

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

[2] Univ New Mexico, Dept Math & Stat, 311 Terrace St NE,MSC01 1115, Albuquerque, NM 87106 USA

关键词: Widom factors;    Szego class;    Equilibrium measure;    Extremal polynomials;    Jacobi polynomials;    Isospectral torus;   

DOI  :  10.1016/j.jmaa.2019.123729

来源: Elsevier

【 摘 要 】

We derive lower bounds for the L-P (mu) norms of monic extremal polynomials with respect to compactly supported probability measures mu. We obtain a sharp universal lower bound for all 0 < p < infinity and all measures in the Szego class and an improved lower bound on L-2(mu) norm for several classes of orthogonal polynomials including Jacobi polynomials, isospectral torus of a finite gap set, and orthogonal polynomials with respect to the equilibrium measure of an arbitrary non-polar compact subset of R. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free