Spectral decomposition and matrix-valued orthogonal polynomials

被引：11

作者：

Groenevelt, Wolter ^{[1
]}

Ismail, Mourad E. H. ^{[2
,3
]}

Koelink, Erik ^{[4
]}

机构：

[1] Delft Univ Technol, DIAM, EWI, NL-2600 GA Delft, Netherlands

[2] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[3] King Saud Univ, Riyadh, Saudi Arabia

[4] Radboud Univ Nijmegen, IMAPP, FNWI, NL-6525 AJ Nijmegen, Netherlands

来源：

ADVANCES IN MATHEMATICS | 2013年 / 244卷

关键词：

Matrix-valued orthogonal polynomials; Spectral theory; ASKEY-WILSON POLYNOMIALS; SPHERICAL-FUNCTIONS; SU(2);

D O I：

10.1016/j.aim.2013.04.025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from scalar-valued orthogonal polynomials is presented. Two examples of matrix-valued orthogonal polynomials with explicit orthogonality relations and three-term recurrence relation are presented, which both can be considered as 2 x 2-matrix-valued analogues of subfamilies of Askey-Wilson polynomials. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：91 / 105

页数：15

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