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dc.contributor.author
Koelink, Erik
dc.contributor.author
de los Ríos, Ana M.
dc.contributor.author
Román, Pablo Manuel
dc.date.available
2018-09-19T17:56:26Z
dc.date.issued
2017-12
dc.identifier.citation
Koelink, Erik; de los Ríos, Ana M.; Román, Pablo Manuel; Matrix-Valued Gegenbauer-Type polynomials; Springer; Constructive Approximation; 46; 3; 12-2017; 459-487
dc.identifier.issn
0176-4276
dc.identifier.uri
http://hdl.handle.net/11336/60249
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Darboux Factorization
dc.subject
Gegenbauer Polynomials
dc.subject
Matrix-Valued Differential Operators
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Matrix-Valued Orthogonal Polynomials
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Shift Operator
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Matrix-Valued Gegenbauer-Type polynomials
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-09-14T19:04:18Z
dc.identifier.eissn
1432-0940
dc.journal.volume
46
dc.journal.number
3
dc.journal.pagination
459-487
dc.journal.pais
Alemania
dc.description.fil
Fil: Koelink, Erik. Radboud Universiteit Nijmegen; Países Bajos
dc.description.fil
Fil: de los Ríos, Ana M.. Universidad de Sevilla; España
dc.description.fil
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
Constructive Approximation
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00365-017-9384-4
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00365-017-9384-4
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