Publication
Relative asymptotics for orthogonal matrix polynomials
| datacite.subject.sdg | 03:Saúde de Qualidade | |
| datacite.subject.sdg | 07:Energias Renováveis e Acessíveis | |
| datacite.subject.sdg | 11:Cidades e Comunidades Sustentáveis | |
| dc.contributor.author | Branquinho, A. | |
| dc.contributor.author | Marcellán, F. | |
| dc.contributor.author | Mendes, A. | |
| dc.date.accessioned | 2025-11-24T15:13:02Z | |
| dc.date.available | 2025-11-24T15:13:02Z | |
| dc.date.issued | 2012-10 | |
| dc.description.abstract | In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We study the generalized matrix Chebyshev polynomials and we deduce its explicit expression as well as we show some illustrative examples. The concept of a Dirac delta functional is introduced. We show how the vector model that includes a Dirac delta functional is a representation of a discrete Sobolev inner product. It also allows to reinterpret such perturbations in the usual matrix Nevai class. Finally, the relative asymptotics between a polynomial in the generalized matrix Nevai class and a polynomial that is orthogonal to a modification of the corresponding matrix measure by the addition of a Dirac delta functional is deduced. © 2012 Elsevier Ltd. All rights reserved. | eng |
| dc.description.sponsorship | The work of the authors has been supported by CMUC and FCT (Portugal), through European program COMPETE/FEDER. | |
| dc.description.sponsorship | The work of the author has been supported by Dirección General de Investigación, Ministerio de Ciencia e Innovación of Spain, grant MTM2009-12740-C03-01. | |
| dc.identifier.citation | A. Branquinho, F. Marcellán, A. Mendes, Relative asymptotics for orthogonal matrix polynomials, Linear Algebra and its Applications, Volume 437, Issue 7, 2012, Pages 1458-1481, ISSN 0024-3795, https://doi.org/10.1016/j.laa.2012.04.032. | |
| dc.identifier.doi | 10.1016/j.laa.2012.04.032 | |
| dc.identifier.issn | 0024-3795 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/14716 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Elsevier | |
| dc.relation.hasversion | https://www.sciencedirect.com/science/article/pii/S0024379512003084?via%3Dihub | |
| dc.relation.ispartof | Linear Algebra and its Applications | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Asymptotic results | |
| dc.subject | Linear functional | |
| dc.subject | Matrix orthogonal polynomials | |
| dc.subject | Nevai class | |
| dc.subject | Recurrence relation | |
| dc.subject | Tridiagonal operator | |
| dc.title | Relative asymptotics for orthogonal matrix polynomials | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 1481 | |
| oaire.citation.issue | 7 | |
| oaire.citation.startPage | 1458 | |
| oaire.citation.title | Linear Algebra and its Applications | |
| oaire.citation.volume | 437 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Mendes | |
| person.givenName | Ana | |
| person.identifier.ciencia-id | 3C19-42EA-DDBD | |
| person.identifier.orcid | 0000-0002-4161-6130 | |
| person.identifier.scopus-author-id | 55873199300 | |
| relation.isAuthorOfPublication | 3523e160-c260-47a6-89cc-eb3fca0059d9 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3523e160-c260-47a6-89cc-eb3fca0059d9 |