Spectral transforms of measures and orthogonal polynomials on regions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:407

Article

Mina-Diaz, Erwin¹  Simanek, Brian² 

[1] Univ Mississippi, Dept Math, University, MS 38677 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

关键词: Orthogonal polynomials;    Strong asymptotics;    Geronimus transform;    Christoffel transform;    Uvarov transform;   

DOI  :  10.1016/j.jmaa.2013.05.035

来源: Elsevier

【 摘 要 】

We discuss Szego-type strong asymptotics for polynomials orthogonal over a region bounded by an analytic curve, and find necessary conditions for such asymptotics to hold on an interior neighborhood of the curve. We also prove that this property is not destroyed when the measure is perturbed by multiplication by a rational function and the addition of point masses. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free