Bispectral Jacobi type polynomials

被引：1

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

[21] ON A DIFFERENTIAL-EQUATION FOR KOORNWINDERS GENERALIZED LAGUERRE-POLYNOMIALS [J].

KOEKOEK, J ;

KOEKOEK, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (04) :1045-1054

[22] On differential equations for Sobolev-type Laguerre polynomials [J].

Koekoek, J ;

Koekoek, R ;

Bavinck, H .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (01) :347-393

[23] Differential equations for generalized Jacobi polynomials [J].

Koekoek, J ;

Koekoek, R .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2000, 126 (1-2) :1-31

[24] DIFFERENTIAL-EQUATIONS FOR SYMMETRICAL GENERALIZED ULTRASPHERICAL POLYNOMIALS [J].

KOEKOEK, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 345 (01) :47-72

[25]

Krall H.L., 1940, The Pennsylvania State College Studies, V6

[26]

Littlejohn L.L, 1986, QUAEST MATH, V10, P49, DOI DOI 10.1080/16073606.1986.9631591

[27]

Littlejohn L.L., 1982, QUAEST MATH, V5, P255

[28]

Shen J, 2011, SPR SER COMPUT MATH, V41, P1, DOI 10.1007/978-3-540-71041-7

[29] A method of constructing Krall's polynomials [J].

Zhedanov, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1999, 107 (01) :1-20

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