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dc.contributor.author
Deaño, Alfredo
dc.contributor.author
Kuijlaars, Arno B. J.
dc.contributor.author
Román, Pablo Manuel
dc.date.available
2024-02-07T12:22:22Z
dc.date.issued
2023-06
dc.identifier.citation
Deaño, Alfredo; Kuijlaars, Arno B. J.; Román, Pablo Manuel; Asymptotics of matrix valued orthogonal polynomials on [−1,1]; Academic Press Inc Elsevier Science; Advances in Mathematics; 423; 6-2023; 1-61
dc.identifier.issn
0001-8708
dc.identifier.uri
http://hdl.handle.net/11336/226119
dc.description.abstract
We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann–Hilbert formulation for MVOPs and the Deift–Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in different regions of the complex plane (outside the interval of orthogonality, on the interval away from the endpoints and in neighborhoods of the endpoints), as well as for the matrix coefficients in the three-term recurrence relation for these MVOPs. The asymptotic analysis follows the work of Kuijlaars, McLaughlin, Van Assche and Vanlessen on scalar Jacobi-type orthogonal polynomials, but it also requires several different factorizations of the matrix part of the weight, in terms of eigenvalues/eigenvectors and using a matrix Szegő function. We illustrate the results with two main examples, MVOPs of Jacobi and Gegenbauer type, coming from group theory.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
ASYMPTOTIC ANALYSIS
dc.subject
MATRIX ORTHOGONAL POLYNOMIALS
dc.subject
RIEMANN-HILBERT PROBLEMS
dc.subject
STEEPEST DESCENT METHOD
dc.subject.classification
Matemática Pura
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Asymptotics of matrix valued orthogonal polynomials on [−1,1]
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-02-06T13:32:22Z
dc.journal.volume
423
dc.journal.pagination
1-61
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Deaño, Alfredo. Universidad Carlos III de Madrid. Instituto de Salud; España
dc.description.fil
Fil: Kuijlaars, Arno B. J.. Katholikie Universiteit Leuven; Bélgica
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
Advances in Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S000187082300186X
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.aim.2023.109043
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