Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials

The main purpose of this work is the study of algebraic and analytic properties associated with spectral transformations of sequences of matrix orthogonal polynomials with respect to a matrix measure supported either on the unit circle or on the real line. In both frameworks, we study some propertie...

Full description

Autores:
Fuentes, Edinson
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2019
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/76952
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/76952
http://bdigital.unal.edu.co/74016/
Palabra clave:
Matrix measure
Spectral transformation
Matrix orthogonal polynomials on the real line
Matrix orthogonal polynomials on the unit circle
Matrix moments
Szego matrix transformation
Christoffel and Uvarov matrix transformations
Medida matricial
Transformación espectral
Polinomios ortogonales matriciales en la recta real
Polinomios ortogonales matriciales en la circunferencia unidad
Momentos matriciales
Transformación matricial de Szego
Transformación matricial de Christoffel y Uvarov,
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_96d03c4e91241ca9196702c981e5514d
oai_identifier_str oai:repositorio.unal.edu.co:unal/76952
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
dc.title.spa.fl_str_mv Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
title Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
spellingShingle Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
Matrix measure
Spectral transformation
Matrix orthogonal polynomials on the real line
Matrix orthogonal polynomials on the unit circle
Matrix moments
Szego matrix transformation
Christoffel and Uvarov matrix transformations
Medida matricial
Transformación espectral
Polinomios ortogonales matriciales en la recta real
Polinomios ortogonales matriciales en la circunferencia unidad
Momentos matriciales
Transformación matricial de Szego
Transformación matricial de Christoffel y Uvarov,
title_short Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
title_full Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
title_fullStr Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
title_full_unstemmed Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
title_sort Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials
dc.creator.fl_str_mv Fuentes, Edinson
dc.contributor.author.spa.fl_str_mv Fuentes, Edinson
dc.contributor.spa.fl_str_mv Garza Gaona, Luis Enrique
Dueñas Ruiz, Herbert Alonso
dc.subject.proposal.spa.fl_str_mv Matrix measure
Spectral transformation
Matrix orthogonal polynomials on the real line
Matrix orthogonal polynomials on the unit circle
Matrix moments
Szego matrix transformation
Christoffel and Uvarov matrix transformations
Medida matricial
Transformación espectral
Polinomios ortogonales matriciales en la recta real
Polinomios ortogonales matriciales en la circunferencia unidad
Momentos matriciales
Transformación matricial de Szego
Transformación matricial de Christoffel y Uvarov,
topic Matrix measure
Spectral transformation
Matrix orthogonal polynomials on the real line
Matrix orthogonal polynomials on the unit circle
Matrix moments
Szego matrix transformation
Christoffel and Uvarov matrix transformations
Medida matricial
Transformación espectral
Polinomios ortogonales matriciales en la recta real
Polinomios ortogonales matriciales en la circunferencia unidad
Momentos matriciales
Transformación matricial de Szego
Transformación matricial de Christoffel y Uvarov,
description The main purpose of this work is the study of algebraic and analytic properties associated with spectral transformations of sequences of matrix orthogonal polynomials with respect to a matrix measure supported either on the unit circle or on the real line. In both frameworks, we study some properties related with a perturbation of a sequence of matrix moments. We extend to the matrix case some algebraic and analytic properties of matrix orthogonal polynomials on the unit circle, that are known in the scalar case, associated with the Uvarov and Christofeeel matrix transformations of a Hermitian matrix measure supported on the unit circle. We also study properties of block Hessenberg and block CMV matrices associated with sequences of matrix orthonormal polynomials, under certain transformations of the corresponding matrix measure. In addition, we extend to the matrix case some properties of the Szego transformation and then use these properties to analyze its effect on some spectral transformations, focusing on the relationship between the matrix-valued Stieltjes and Carathéodory functions.
publishDate 2019
dc.date.issued.spa.fl_str_mv 2019-09-15
dc.date.accessioned.spa.fl_str_mv 2020-03-30T06:33:53Z
dc.date.available.spa.fl_str_mv 2020-03-30T06:33:53Z
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/76952
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/74016/
url https://repositorio.unal.edu.co/handle/unal/76952
http://bdigital.unal.edu.co/74016/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas
Departamento de Matemáticas
dc.relation.haspart.spa.fl_str_mv 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
dc.relation.references.spa.fl_str_mv Fuentes, Edinson (2019) Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/76952/1/Tesis%20Doctoral%20-%20Edinson%20Fuentes.pdf
https://repositorio.unal.edu.co/bitstream/unal/76952/2/Tesis%20Doctoral%20-%20Edinson%20Fuentes.pdf.jpg
bitstream.checksum.fl_str_mv 943f6a14d6d6c1757825a11a68de290f
bb5a5bf6bbd5440e035f8f6ca28ca70c
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
_version_ 1814089386913955840
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Garza Gaona, Luis EnriqueDueñas Ruiz, Herbert AlonsoFuentes, Edinsone50c4e46-58d1-4cf6-9f01-59bfa83dfa783002020-03-30T06:33:53Z2020-03-30T06:33:53Z2019-09-15https://repositorio.unal.edu.co/handle/unal/76952http://bdigital.unal.edu.co/74016/The main purpose of this work is the study of algebraic and analytic properties associated with spectral transformations of sequences of matrix orthogonal polynomials with respect to a matrix measure supported either on the unit circle or on the real line. In both frameworks, we study some properties related with a perturbation of a sequence of matrix moments. We extend to the matrix case some algebraic and analytic properties of matrix orthogonal polynomials on the unit circle, that are known in the scalar case, associated with the Uvarov and Christofeeel matrix transformations of a Hermitian matrix measure supported on the unit circle. We also study properties of block Hessenberg and block CMV matrices associated with sequences of matrix orthonormal polynomials, under certain transformations of the corresponding matrix measure. In addition, we extend to the matrix case some properties of the Szego transformation and then use these properties to analyze its effect on some spectral transformations, focusing on the relationship between the matrix-valued Stieltjes and Carathéodory functions.Resumen: El objetivo principal de este trabajo es estudiar propiedades algebraicas y analíticas asociadas a transformaciones espectrales de polinomios ortogonales matriciales con respecto a una medida matricial con soporte ya sea sobre la circunferencia unidad o sobre la recta real. En ambos casos, se estudian algunas propiedades relacionadas con una perturbación de una sucesión de momentos matriciales. Extendemos al caso matricial algunas propiedades algebraicas y analíticas de polinomios ortogonales matriciales sobre la circunferencia unidad, que son conocidas en el caso escalar, asociadas con las transformaciones matriciales de Uvarov y Christoffel de una medida matricial Hermitiana con soporte sobre la circunferencia unidad. También estudiamos propiedades de matrices Hessenberg y CMV por bloques, asociadas con sucesiones de polinomios ortonormales matriciales, bajo ciertas transformaciones de la medida matricial correspondiente. Además, se extienden al caso matricial algunas propiedades de la transformación Szego y se utilizan estas propiedades para analizar su efecto sobre algunas transformaciones espectrales, enfocándose en la relación para las funciones a valor matricial de Stieltjes y Carathéodory.Doctoradoapplication/pdfspaUniversidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de MatemáticasDepartamento de Matemáticas5 Ciencias naturales y matemáticas / Science51 Matemáticas / MathematicsFuentes, Edinson (2019) Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomials. Doctorado thesis, Universidad Nacional de Colombia - Sede Bogotá.Algebraic and analytic properties associated with spectral transformations of matrix orthogonal polynomialsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDMatrix measureSpectral transformationMatrix orthogonal polynomials on the real lineMatrix orthogonal polynomials on the unit circleMatrix momentsSzego matrix transformationChristoffel and Uvarov matrix transformationsMedida matricialTransformación espectralPolinomios ortogonales matriciales en la recta realPolinomios ortogonales matriciales en la circunferencia unidadMomentos matricialesTransformación matricial de SzegoTransformación matricial de Christoffel y Uvarov,ORIGINALTesis Doctoral - Edinson Fuentes.pdfapplication/pdf1355572https://repositorio.unal.edu.co/bitstream/unal/76952/1/Tesis%20Doctoral%20-%20Edinson%20Fuentes.pdf943f6a14d6d6c1757825a11a68de290fMD51THUMBNAILTesis Doctoral - Edinson Fuentes.pdf.jpgTesis Doctoral - Edinson Fuentes.pdf.jpgGenerated Thumbnailimage/jpeg4239https://repositorio.unal.edu.co/bitstream/unal/76952/2/Tesis%20Doctoral%20-%20Edinson%20Fuentes.pdf.jpgbb5a5bf6bbd5440e035f8f6ca28ca70cMD52unal/76952oai:repositorio.unal.edu.co:unal/769522023-07-16 23:04:01.084Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co

Publicaciones similares