Mixed-type multiple orthogonal Laurent polynomials on the unit circle

Mixed-type orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss-Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relation...

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Detalles Bibliográficos
Autores: Huertas Cejudo, Edmundo José|||0000-0001-6802-3303, Mañas Baena, Manuel
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/68062
Acceso en línea:http://hdl.handle.net/10017/68062
https://dx.doi.org/10.1016/j.cam.2025.117037
Access Level:acceso abierto
Palabra clave:Mixed-type multiple orthogonal Laurent polynomials
Unit circle
Christoffel-Darboux formulas
ABC theorem
Recurrence relations
Christoffel perturbations
Geronimus perturbations
Matemáticas
Mathematics
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spelling Mixed-type multiple orthogonal Laurent polynomials on the unit circleHuertas Cejudo, Edmundo José|||0000-0001-6802-3303Mañas Baena, ManuelMixed-type multiple orthogonal Laurent polynomialsUnit circleChristoffel-Darboux formulasABC theoremRecurrence relationsChristoffel perturbationsGeronimus perturbationsMatemáticasMathematicsMixed-type orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss-Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel-Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations.Agencia Estatal de InvestigaciónComunidad de MadridElsevier20252025-09-06journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/68062https://dx.doi.org/10.1016/j.cam.2025.117037reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Not available PID2021-122154NB-I00Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Not available PID2024-155133NB-I00Comunidad de Madrid http://dx.doi.org/10.13039/100012818 Not available ;CM%2FJIN%2F2021-014open accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/680622026-06-18T11:13:07Z
dc.title.none.fl_str_mv Mixed-type multiple orthogonal Laurent polynomials on the unit circle
title Mixed-type multiple orthogonal Laurent polynomials on the unit circle
spellingShingle Mixed-type multiple orthogonal Laurent polynomials on the unit circle
Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Mixed-type multiple orthogonal Laurent polynomials
Unit circle
Christoffel-Darboux formulas
ABC theorem
Recurrence relations
Christoffel perturbations
Geronimus perturbations
Matemáticas
Mathematics
title_short Mixed-type multiple orthogonal Laurent polynomials on the unit circle
title_full Mixed-type multiple orthogonal Laurent polynomials on the unit circle
title_fullStr Mixed-type multiple orthogonal Laurent polynomials on the unit circle
title_full_unstemmed Mixed-type multiple orthogonal Laurent polynomials on the unit circle
title_sort Mixed-type multiple orthogonal Laurent polynomials on the unit circle
dc.creator.none.fl_str_mv Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Mañas Baena, Manuel
author Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
author_facet Huertas Cejudo, Edmundo José|||0000-0001-6802-3303
Mañas Baena, Manuel
author_role author
author2 Mañas Baena, Manuel
author2_role author
dc.subject.none.fl_str_mv Mixed-type multiple orthogonal Laurent polynomials
Unit circle
Christoffel-Darboux formulas
ABC theorem
Recurrence relations
Christoffel perturbations
Geronimus perturbations
Matemáticas
Mathematics
topic Mixed-type multiple orthogonal Laurent polynomials
Unit circle
Christoffel-Darboux formulas
ABC theorem
Recurrence relations
Christoffel perturbations
Geronimus perturbations
Matemáticas
Mathematics
description Mixed-type orthogonal Laurent polynomials on the unit circle of CMV type are constructed utilizing a matrix of moments and its Gauss-Borel factorization and employing a multiple extension of the CMV ordering. A systematic analysis of the associated multiple orthogonality and biorthogonality relations, and an examination of the degrees of the Laurent polynomials is given. Recurrence relations, expressed in terms of banded matrices, are found. These recurrence relations lay the groundwork for corresponding Christoffel-Darboux kernels and relations, as well as for elucidating the ABC theorem. The paper also develops the theory of diagonal Christoffel and Geronimus perturbations of the matrix of measures. Christoffel formulas are found for both perturbations.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-09-06
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/68062
https://dx.doi.org/10.1016/j.cam.2025.117037
url http://hdl.handle.net/10017/68062
https://dx.doi.org/10.1016/j.cam.2025.117037
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Not available PID2021-122154NB-I00
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Not available PID2024-155133NB-I00
Comunidad de Madrid http://dx.doi.org/10.13039/100012818 Not available ;CM%2FJIN%2F2021-014
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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