Publication:
Asymptotics of matrix valued orthogonal polynomials on [−1,1]

Simple item page
dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorDeaño Cabrera, Alfredo
dc.contributor.authorKuijlaars, Arno B.J.
dc.contributor.authorRomán, P.
dc.date.accessioned2023-12-21T19:25:09Z
dc.date.available2023-12-21T19:25:09Z
dc.date.issued2023-06-15
dc.description.abstractWe 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.En
dc.description.sponsorshipComunidad de Madrid (Spain). CM/JIN/2021-014es
dc.description.sponsorshipacknowledges financial support from Dirección General de Investigación e Innovación, Consejería de Educación e Investigación of Comunidad de Madrid (Spain), and Universidad de Alcalá under grant CM/JIN/2021-014, and Comunidad de Madrid (Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). Research supported by Grant PID2021-123969NB-I00, funded by MCIN/AEI/10.13039/501100011033, and by grant PID2021-122154NB-I00 from Spanish Agencia Estatal de Investigación. A. D. acknowledges financial support and hospitality from IMAPP, Radboud Universiteit Nijmegen, and in particular Prof. Erik Koelink, during a visit to Nijmegen in June 2022.En
dc.description.sponsorshipGobierno de España. MCIN/AEI/10.13039/501100011033Es
dc.description.sponsorshipGobierno de España. PID2021-122154NB-I00
dc.description.statusPublicadoes
dc.format.extent61
dc.identifier.bibliographicCitationAdvances in Mathematics, 423, 109043En
dc.identifier.doihttps://doi.org/10.1016/j.aim.2023.109043
dc.identifier.issn0001-8708
dc.identifier.publicationfirstpage1es
dc.identifier.publicationissue109043es
dc.identifier.publicationlastpage61es
dc.identifier.publicationtitleAdvances in mathematicsEn
dc.identifier.publicationvolume423
dc.identifier.urihttps://hdl.handle.net/10016/39150
dc.identifier.uxxiAR/0000033593
dc.language.isoeng
dc.publisherElsevier Inc
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/pii/S000187082300186X?via%3Dihub
dc.rights© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).En
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessEn
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherMatrix orthogonal polynomialsEn
dc.subject.otherAsymptotic analysisEn
dc.subject.otherRiemann-Hilbert problemsEn
dc.subject.otherSteepest descent methodEn
dc.titleAsymptotics of matrix valued orthogonal polynomials on [−1,1]En
dc.typeresearch articleen
dc.type.hasVersionVoREn
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
asymptotics_ADVANCES_2023.pdf
Size:
1010.88 KB
Format:
Adobe Portable Document Format
Download
Collections
DM - GAMA - Artículos de Revistas