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Propiedades de algunos sistemas de polinomios ortogonales Sobolev en varias variables

dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.contributor.advisorDueñas Ruiz, Herbert Alonso
dc.contributor.authorSalazar Morales, Omar
dc.date.accessioned2022-08-09T21:04:55Z
dc.date.available2022-08-09T21:04:55Z
dc.date.issued2022-02-01
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/81829
dc.descriptionTexto, ecuaciones, fórmulas
dc.descriptionformúlas matemáticas
dc.description.abstractEn este trabajo estudiamos algunas propiedades algebraicas y analíticas de los polinomios ortogonales en varias variables reales con respecto a un producto interno Sobolev continuo-discreto. Consideramos los polinomios Sobolev sobre diferentes dominios, a saber: un dominio producto; la bola unitaria; el simplex; y el cono. Nuestros principales resultados consisten en un método iterativo de construcción de los polinomios ortogonales con respecto al producto interno, propiedades que involucran su parte principal (continua), una fórmula de conexión, y algunos resultados sobre ecuaciones diferenciales parciales. Con el fin de ilustrar nuestras principales ideas, al final de este trabajo presentamos varios ejemplos numéricos en dos variables. Además, discutimos algunos problemas abiertos.
dc.description.abstractIn this work we study some algebraic and analytical properties of the orthogonal polynomials in several real variables with respect to a continuous-discrete Sobolev inner product. We consider the Sobolev polynomials on different domains, namely: a product domain; the unit ball; the simplex; and the cone. Our main results consist of an iterative method for constructing the orthogonal polynomials, properties that involve the main (continuous) part of this inner product, a connection formula, and some results on partial differential equations. In order to illustrate our main ideas, at the end of this work we present some numerical examples in two variables. In addition, we discuss some open problems.
dc.description.sponsorshipFacultad de Ciencias, Sede Bogotá
dc.format.extentvii, 137 páginas
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherUniversidad Nacional de Colombia
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc510 - Matemáticas::515 - Análisis
dc.titlePropiedades de algunos sistemas de polinomios ortogonales Sobolev en varias variables
dc.typeTrabajo de grado - Doctorado
dc.type.driverinfo:eu-repo/semantics/doctoralThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.publisher.programBogotá - Ciencias - Doctorado en Ciencias - Matemáticas
dc.contributor.researchgroupGrupo de Investigación en Polinomios Ortogonales y Aplicaciones
dc.description.degreelevelDoctorado
dc.description.degreenameDoctor en Ciencias - Matemáticas
dc.description.researchareaPolinomios ortogonales en varias variables
dc.identifier.instnameUniversidad Nacional de Colombia
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourlhttps://repositorio.unal.edu.co/
dc.publisher.departmentDepartamento de Matemáticas
dc.publisher.facultyFacultad de Ciencias
dc.publisher.placeBogotá, Colombia
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotá
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccess
dc.subject.proposalPolinomios ortogonales
dc.subject.proposalPolinomios Sobolev
dc.subject.proposalPolinomios en varias variables
dc.subject.proposalProductos internos
dc.subject.proposalProductos internos Sobolev
dc.subject.proposalEcuaciones diferenciales
dc.subject.proposalEcuaciones diferenciales parciales
dc.subject.proposalOrthogonal polynomials
dc.subject.proposalSobolev polynomials
dc.subject.proposalPolynomials in several variables
dc.subject.proposalInner products
dc.subject.proposalSobolev inner products
dc.subject.proposalDifferential equations
dc.subject.proposalPartial differential equations
dc.title.translatedProperties of some Sobolev orthogonal polynomial systems in several variables
dc.type.coarhttp://purl.org/coar/resource_type/c_db06
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.redcolhttp://purl.org/redcol/resource_type/TD
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2
oaire.awardtitleSobre polinomios ortogonales en varias variables, polinomios ortogonales matriciales y pares coherentes de polinomios ortogonales
dcterms.audience.professionaldevelopmentEstudiantes
dcterms.audience.professionaldevelopmentInvestigadores
dcterms.audience.professionaldevelopmentMaestros
dcterms.audience.professionaldevelopmentPadres y familias
dcterms.audience.professionaldevelopmentPúblico general


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