Reducibility of matrix weights

Autores
Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we discuss the notion of reducibility of matrix weights and introduce a real vector space CR which encodes all information about the reducibility of W. In particular, a weight W reduces if and only if there is a nonscalar matrix T such that TW= WT∗. Also, we prove that reducibility can be studied by looking at the commutant of the monic orthogonal polynomials or by looking at the coefficients of the corresponding three-term recursion relation. A matrix weight may not be expressible as direct sum of irreducible weights, but it is always equivalent to a direct sum of irreducible weights. We also establish that the decompositions of two equivalent weights as sums of irreducible weights have the same number of terms and that, up to a permutation, they are equivalent. We consider the algebra of right-hand-side matrix differential operators D(W) of a reducible weight W, giving its general structure. Finally, we make a change of emphasis by considering the reducibility of polynomials, instead of reducibility of matrix weights.
Fil: Tirao, Juan Alfredo. 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
Fil: Zurrián, Ignacio Nahuel. 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
Materia
COMPLETE REDUCIBILITY
MATRIX ORTHOGONAL POLYNOMIALS
REDUCIBLE WEIGHTS
THE ALGEBRA OF A REDUCIBLE WEIGHT
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/58367

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spelling Reducibility of matrix weightsTirao, Juan AlfredoZurrián, Ignacio NahuelCOMPLETE REDUCIBILITYMATRIX ORTHOGONAL POLYNOMIALSREDUCIBLE WEIGHTSTHE ALGEBRA OF A REDUCIBLE WEIGHThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we discuss the notion of reducibility of matrix weights and introduce a real vector space CR which encodes all information about the reducibility of W. In particular, a weight W reduces if and only if there is a nonscalar matrix T such that TW= WT∗. Also, we prove that reducibility can be studied by looking at the commutant of the monic orthogonal polynomials or by looking at the coefficients of the corresponding three-term recursion relation. A matrix weight may not be expressible as direct sum of irreducible weights, but it is always equivalent to a direct sum of irreducible weights. We also establish that the decompositions of two equivalent weights as sums of irreducible weights have the same number of terms and that, up to a permutation, they are equivalent. We consider the algebra of right-hand-side matrix differential operators D(W) of a reducible weight W, giving its general structure. Finally, we make a change of emphasis by considering the reducibility of polynomials, instead of reducibility of matrix weights.Fil: Tirao, Juan Alfredo. 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; ArgentinaFil: Zurrián, Ignacio Nahuel. 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; ArgentinaSpringer2018-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/58367Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Reducibility of matrix weights; Springer; Ramanujan Journal; 45; 2; 2-2018; 349-3741382-4090CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11139-016-9834-9info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11139-016-9834-9info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.04059info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:04:56Zoai:ri.conicet.gov.ar:11336/58367instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:04:57.057CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Reducibility of matrix weights
title Reducibility of matrix weights
spellingShingle Reducibility of matrix weights
Tirao, Juan Alfredo
COMPLETE REDUCIBILITY
MATRIX ORTHOGONAL POLYNOMIALS
REDUCIBLE WEIGHTS
THE ALGEBRA OF A REDUCIBLE WEIGHT
title_short Reducibility of matrix weights
title_full Reducibility of matrix weights
title_fullStr Reducibility of matrix weights
title_full_unstemmed Reducibility of matrix weights
title_sort Reducibility of matrix weights
dc.creator.none.fl_str_mv Tirao, Juan Alfredo
Zurrián, Ignacio Nahuel
author Tirao, Juan Alfredo
author_facet Tirao, Juan Alfredo
Zurrián, Ignacio Nahuel
author_role author
author2 Zurrián, Ignacio Nahuel
author2_role author
dc.subject.none.fl_str_mv COMPLETE REDUCIBILITY
MATRIX ORTHOGONAL POLYNOMIALS
REDUCIBLE WEIGHTS
THE ALGEBRA OF A REDUCIBLE WEIGHT
topic COMPLETE REDUCIBILITY
MATRIX ORTHOGONAL POLYNOMIALS
REDUCIBLE WEIGHTS
THE ALGEBRA OF A REDUCIBLE WEIGHT
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we discuss the notion of reducibility of matrix weights and introduce a real vector space CR which encodes all information about the reducibility of W. In particular, a weight W reduces if and only if there is a nonscalar matrix T such that TW= WT∗. Also, we prove that reducibility can be studied by looking at the commutant of the monic orthogonal polynomials or by looking at the coefficients of the corresponding three-term recursion relation. A matrix weight may not be expressible as direct sum of irreducible weights, but it is always equivalent to a direct sum of irreducible weights. We also establish that the decompositions of two equivalent weights as sums of irreducible weights have the same number of terms and that, up to a permutation, they are equivalent. We consider the algebra of right-hand-side matrix differential operators D(W) of a reducible weight W, giving its general structure. Finally, we make a change of emphasis by considering the reducibility of polynomials, instead of reducibility of matrix weights.
Fil: Tirao, Juan Alfredo. 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
Fil: Zurrián, Ignacio Nahuel. 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
description In this paper, we discuss the notion of reducibility of matrix weights and introduce a real vector space CR which encodes all information about the reducibility of W. In particular, a weight W reduces if and only if there is a nonscalar matrix T such that TW= WT∗. Also, we prove that reducibility can be studied by looking at the commutant of the monic orthogonal polynomials or by looking at the coefficients of the corresponding three-term recursion relation. A matrix weight may not be expressible as direct sum of irreducible weights, but it is always equivalent to a direct sum of irreducible weights. We also establish that the decompositions of two equivalent weights as sums of irreducible weights have the same number of terms and that, up to a permutation, they are equivalent. We consider the algebra of right-hand-side matrix differential operators D(W) of a reducible weight W, giving its general structure. Finally, we make a change of emphasis by considering the reducibility of polynomials, instead of reducibility of matrix weights.
publishDate 2018
dc.date.none.fl_str_mv 2018-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/58367
Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Reducibility of matrix weights; Springer; Ramanujan Journal; 45; 2; 2-2018; 349-374
1382-4090
CONICET Digital
CONICET
url http://hdl.handle.net/11336/58367
identifier_str_mv Tirao, Juan Alfredo; Zurrián, Ignacio Nahuel; Reducibility of matrix weights; Springer; Ramanujan Journal; 45; 2; 2-2018; 349-374
1382-4090
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11139-016-9834-9
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11139-016-9834-9
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1501.04059
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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