On multivariate orthogonal polynomials and elementary symmetric functions

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dc.contributor.authorBracciali, Cleonice F. [UNESP]
dc.contributor.authorPiñar, Miguel A.
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.contributor.institutionFacultad de Ciencias. Universidad de Granada
dc.date.accessioned2023-07-29T13:26:56Z
dc.date.available2023-07-29T13:26:56Z
dc.date.issued2023-01-01
dc.description.abstractWe study families of multivariate orthogonal polynomials with respect to the symmetric weight function in d variables Bγ(x)=∏i=1dω(xi)∏i<j|xi-xj|2γ+1,x∈(a,b)d,for γ> - 1 , where ω(t) is an univariate weight function in t∈ (a, b) and x= (x1, x2, … , xd) with xi∈ (a, b). Applying the change of variables xi, i= 1 , 2 , … , d, into ur, r= 1 , 2 , … , d, where ur is the r-th elementary symmetric function, we obtain the domain region in terms of the discriminant of the polynomials having xi, i= 1 , 2 , … , d, as its zeros and in terms of the corresponding Sturm sequence. Choosing the univariate weight function as the Hermite, Laguerre, and Jacobi weight functions, we obtain the representation in terms of the variables ur for the partial differential operators such that the respective Hermite, Laguerre, and Jacobi generalized multivariate orthogonal polynomials are the eigenfunctions. Finally, we present explicitly the partial differential operators for Hermite, Laguerre, and Jacobi generalized polynomials, for d= 2 and d= 3 variables.en
dc.description.affiliationDepartamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, SP
dc.description.affiliationInstituto de Matemáticas IMAG & Departamento de Matemática Aplicada Facultad de Ciencias. Universidad de Granada
dc.description.affiliationUnespDepartamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, SP
dc.description.sponsorshipUniversidad de Granada
dc.description.sponsorshipVicerrectorado de Investigación y Transferencia, Universidad de Granada
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipAgencia Estatal de Investigación
dc.description.sponsorshipMinisterio de Ciencia, Innovación y Universidades
dc.description.sponsorshipIdCAPES: 88887.468471/2019-00
dc.description.sponsorshipIdAgencia Estatal de Investigación: CEX2020-001105-M/AEI/10.13039/501100011033
dc.description.sponsorshipIdMinisterio de Ciencia, Innovación y Universidades: PGC2018-094932-B-I00
dc.format.extent183-206
dc.identifierhttp://dx.doi.org/10.1007/s11075-022-01434-4
dc.identifier.citationNumerical Algorithms, v. 92, n. 1, p. 183-206, 2023.
dc.identifier.doi10.1007/s11075-022-01434-4
dc.identifier.issn1572-9265
dc.identifier.issn1017-1398
dc.identifier.scopus2-s2.0-85141170199
dc.identifier.urihttp://hdl.handle.net/11449/247828
dc.language.isoeng
dc.relation.ispartofNumerical Algorithms
dc.sourceScopus
dc.subjectElementary symmetric functions
dc.subjectMultivariate orthogonal polynomials
dc.subjectSymmetric polynomials
dc.titleOn multivariate orthogonal polynomials and elementary symmetric functionsen
dc.typeArtigo
unesp.author.orcid0000-0001-6210-4567[2]

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Artigos - Matemática - IBILCE