A matrix characterization for the Dv-semiclassical and Dv-coherent orthogonal polynomials

被引：0

作者：

Garza, Lino G. ^{[1
]}

Garza, Luis E. ^{[2
]}

Marcellan, Francisco ^{[1
,3
]}

Pinzon-Cortes, Natalia C. ^{[4
]}

机构：

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] Univ Colima, Fac Ciencias, Colima 28045, Mexico

[3] Inst Ciencias Matemat ICMAT, Madrid, Spain

[4] Univ Nacl Colombia, Fac Ciencias, Dept Matemat, Bogota, Colombia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 487卷

关键词：

Semiclassical discrete orthogonal polynomials; Matrix representation; Structure relation; D-v-coherent pairs; LINEAR FUNCTIONALS; N)-COHERENT PAIRS; (M;

D O I：

10.1016/j.laa.2015.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a new structure relation for the sequence of orthogonal polynomials associated with a D-v-semiclassical linear functional of class s, and then we use it to obtain a matrix characterization of the D-v-semiclassical orthogonal polynomials in terms of the Jacobi matrix associated with the multiplication operator in the basis of orthonormal polynomials, and the nonsingular lower triangular matrix that represents the orthogonal polynomials with respect to some bases of polynomials. We also provide a matrix characterization of D-v-coherent pairs of linear functionals. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：242 / 259

页数：18

共 11 条

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Garza, Luis E.
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[8] Characterization and construction of classical orthogonal polynomials using a matrix approach
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[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (09) : 3635 - 3648
[9] Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization
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[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2011, 7
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