Artículo
Matrix-Valued Gegenbauer-Type polynomials
Fecha de publicación:
12/2017
Editorial:
Springer
Revista:
Constructive Approximation
ISSN:
0176-4276
e-ISSN:
1432-0940
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter ν> 0. The LDU-decomposition of the weight is explicitly given in terms of Gegenbauer polynomials. We establish a matrix-valued Pearson equation for these matrix weights leading to explicit shift operators relating the weights for parameters ν and ν+ 1. The matrix coefficients of the Pearson equation are obtained using a special matrix-valued differential operator in a commutative algebra of symmetric differential operators. The corresponding orthogonal polynomials are the matrix-valued Gegenbauer-type polynomials which are eigenfunctions of the symmetric matrix-valued differential operators. Using the shift operators, we find the squared norm, and we establish a simple Rodrigues formula. The three-term recurrence relation is obtained explicitly using the shift operators as well. We give an explicit nontrivial expression for the matrix entries of the matrix-valued Gegenbauer-type polynomials in terms of scalar-valued Gegenbauer and Racah polynomials using the LDU-decomposition and differential operators. The case ν= 1 reduces to the case of matrix-valued Chebyshev polynomials previously obtained using group theoretic considerations.
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Koelink, Erik; de los Ríos, Ana M.; Román, Pablo Manuel; Matrix-Valued Gegenbauer-Type polynomials; Springer; Constructive Approximation; 46; 3; 12-2017; 459-487
Compartir
Altmétricas