Propiedades de algunos sistemas de polinomios ortogonales Sobolev en varias variables

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dc.contributor.advisorDueñas Ruiz, Herbert Alonso
dc.contributor.authorSalazar Morales, Omar
dc.contributor.researchgroupGrupo de Investigación en Polinomios Ortogonales y Aplicacionesspa
dc.date.accessioned2022-08-09T21:04:55Z
dc.date.available2022-08-09T21:04:55Z
dc.date.issued2022-02-01
dc.descriptionTexto, ecuaciones, fórmulasspa
dc.descriptionformúlas matemáticasspa
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.spa
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.eng
dc.description.degreelevelDoctoradospa
dc.description.degreenameDoctor en Ciencias - Matemáticasspa
dc.description.researchareaPolinomios ortogonales en varias variablesspa
dc.description.sponsorshipFacultad de Ciencias, Sede Bogotáspa
dc.format.extentvii, 137 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/81829
dc.language.isoengspa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotáspa
dc.publisher.departmentDepartamento de Matemáticasspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeBogotá, Colombiaspa
dc.publisher.programBogotá - Ciencias - Doctorado en Ciencias - Matemáticasspa
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dc.relation.referencesXu, Yuan. “Approximation and orthogonality in Sobolev spaces on a triangle”. In: Constr. Approx. 46.2 (2017), pp. 349–434.spa
dc.relation.referencesXu, Yuan. “Orthogonal polynomials and Fourier orthogonal series on a cone”. In: J. Fourier Anal. Appl. 26.3 (2020). Paper 36, pp. 1–42spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/spa
dc.subject.ddc510 - Matemáticas::515 - Análisisspa
dc.subject.proposalPolinomios ortogonalesspa
dc.subject.proposalPolinomios Sobolevspa
dc.subject.proposalPolinomios en varias variablesspa
dc.subject.proposalProductos internosspa
dc.subject.proposalProductos internos Sobolevspa
dc.subject.proposalEcuaciones diferencialesspa
dc.subject.proposalEcuaciones diferenciales parcialesspa
dc.subject.proposalOrthogonal polynomialseng
dc.subject.proposalSobolev polynomialseng
dc.subject.proposalPolynomials in several variableseng
dc.subject.proposalInner productseng
dc.subject.proposalSobolev inner productseng
dc.subject.proposalDifferential equationseng
dc.subject.proposalPartial differential equationseng
dc.titlePropiedades de algunos sistemas de polinomios ortogonales Sobolev en varias variablesspa
dc.title.translatedProperties of some Sobolev orthogonal polynomial systems in several variableseng
dc.typeTrabajo de grado - Doctoradospa
dc.type.coarhttp://purl.org/coar/resource_type/c_db06spa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/doctoralThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TDspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
dcterms.audience.professionaldevelopmentEstudiantesspa
dcterms.audience.professionaldevelopmentInvestigadoresspa
dcterms.audience.professionaldevelopmentMaestrosspa
dcterms.audience.professionaldevelopmentPadres y familiasspa
dcterms.audience.professionaldevelopmentPúblico generalspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa
oaire.awardtitleSobre polinomios ortogonales en varias variables, polinomios ortogonales matriciales y pares coherentes de polinomios ortogonalesspa

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