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dc.contributor.author
Ismail, Mourad E. H.
dc.contributor.author
Koelink, Erik
dc.contributor.author
Román, Pablo Manuel
dc.date.available
2020-12-17T13:49:09Z
dc.date.issued
2019-09
dc.identifier.citation
Ismail, Mourad E. H.; Koelink, Erik; Román, Pablo Manuel; Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice; Academic Press Inc Elsevier Science; Advances In Applied Mathematics; 110; 9-2019; 235-269
dc.identifier.issn
0196-8858
dc.identifier.uri
http://hdl.handle.net/11336/120729
dc.description.abstract
A general family of matrix valued Hermite type orthogonal polynomials is introduced as the matrix orthogonal polynomials with respect to a weight. The matrix polynomials are eigenfunctions of a matrix differential equation. For the weight we derive Pearson equations, which allow us to derive many explicit properties of these matrix polynomials. In particular, the matrix polynomials are eigenfunctions to another matrix differential equation. We also obtain for these polynomials shift operators, a Rodrigues formula, explicit expressions for the squared norm, explicit three term recurrence relations, etc. The matrix entries of the matrix polynomials can be expressed in terms of scalar Hermite and dual Hahn polynomials. We also derive a connection formula for the matrix Hermite polynomials. Next we show that operational Burchnall formulas extend to matrix polynomials. We make this explicit for the matrix Hermite polynomials and for previously introduced matrix Gegenbauer type orthogonal polynomials. The Burchnall approach gives two descriptions of the matrix valued orthogonal polynomials for the Toda modification of the matrix Hermite weight. In particular, we obtain an explicit non-trivial solution to the non-abelian Toda lattice equations.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
BURCHNALL IDENTITIES
dc.subject
MATRIX ORTHOGONAL POLYNOMIALS
dc.subject
NON-ABELIAN TODA LATTICE
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-19T21:18:27Z
dc.journal.volume
110
dc.journal.pagination
235-269
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Ismail, Mourad E. H.. University Of Central Florida; Estados Unidos
dc.description.fil
Fil: Koelink, Erik. Radboud Universiteit; Países Bajos
dc.description.fil
Fil: Román, Pablo Manuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. 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
Advances In Applied Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1016/j.aam.2019.07.002
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0196885819301034
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