On three-term recurrence and Christoffel-Darboux identity for orthogonal rational functions on the real line

被引：0

作者：

Sun, Ye-Peng ^{[1
]}

Chang, Xiang-Ke ^{[2
]}

He, Yi ^{[3
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan, Peoples R China

[2] Chinese Acad Sci, AMSS, Inst Computat Math & Sci Engn Comp, LSEC, Beijing, Peoples R China

[3] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan, Peoples R China

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2016年 / 27卷 / 04期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

33C45; 11C20; three-term recurrence; Christoffel-Darboux relation; Orthogonal rational functions;

D O I：

10.1080/10652469.2015.1118097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

First, we give an algebraic proof to the Christoffel-Darboux identity of formal orthogonal rational functions on the real line by exposing some underlying algebraic properties. This proof does not involve the three-term recurrence relationship. Besides, it is shown that if a family of rational functions satisfies the Christoffel-Darboux relation, then it also admits a three-term recurrence relationship. Thus, the equivalence between both relations is revealed.

引用

页码：268 / 280

页数：13

共 27 条

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