Bispectral Jacobi type polynomials

被引：0

作者：

Duran, Antonio J. ^{[1
]}

de la Iglesia, Manuel D. ^{[2
]}

机构：

[1] Univ Seville, Dept Anal Matemat, Apdo POB 1160, Seville 41080, Spain

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico

来源：

ADVANCES IN APPLIED MATHEMATICS | 2022年 / 136卷

关键词：

Orthogonal polynomials; Bispectral orthogonal polynomials; Recurrence relations; Krall polynomials; Jacobi polynomials; DIFFERENTIAL-EQUATIONS; COMMUTATIVE ALGEBRAS;

D O I：

10.1016/j.aam.2022.102322

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi type polynomials include, as particular cases, the Krall-Jacobi polynomials. As the main results we prove that the Jacobi type polynomials always satisfy higher-order recurrence relations (i.e., they are bispectral). We also prove that the Krall-Jacobi families are the only Jacobi type polynomials which are orthogonal with respect to a measure on the real line. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：35

共 29 条

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