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
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/58367
Ver los metadatos del registro completo
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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 Técnicas2025-10-22T11:34:37Zoai: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:34982025-10-22 11:34:37.531CONICET 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 |
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2018-02 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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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 |
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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 |
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eng |
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eng |
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