On the existence of orthogonal polynomials for oscillatory weights on a bounded interval

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Majidian, Hassan

关键词: Orthogonal polynomial;    Oscillatory weight;    Gaussian quadrature rule;   

DOI  :  10.1016/j.jmaa.2015.02.017

来源: Elsevier

【 摘 要 】

It is shown that the polynomials orthogonal on (-1,1) w.r.t. the oscillatory weight e(i omega x) exist if omega is a transcendental number and tan omega/omega is an element of Q. Also, it is proved that such orthogonal polynomials exist for almost all omega > 0, and the roots are all simple if omega > 0 is either small enough or large enough. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free