On multivariate orthogonal polynomials and elementary symmetric functions
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
DOI: | 10.1007/s11075-022-01434-4 |
Texto Completo: | http://dx.doi.org/10.1007/s11075-022-01434-4 http://hdl.handle.net/11449/247828 |
Resumo: | We 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. |
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On multivariate orthogonal polynomials and elementary symmetric functionsElementary symmetric functionsMultivariate orthogonal polynomialsSymmetric polynomialsWe 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.Universidad de GranadaVicerrectorado de Investigación y Transferencia, Universidad de GranadaCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Agencia Estatal de InvestigaciónMinisterio de Ciencia, Innovación y UniversidadesDepartamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, SPInstituto de Matemáticas IMAG & Departamento de Matemática Aplicada Facultad de Ciencias. Universidad de GranadaDepartamento de Matemática IBILCE UNESP - Universidade Estadual Paulista, SPCAPES: 88887.468471/2019-00Agencia Estatal de Investigación: CEX2020-001105-M/AEI/10.13039/501100011033Ministerio de Ciencia, Innovación y Universidades: PGC2018-094932-B-I00Universidade Estadual Paulista (UNESP)Facultad de Ciencias. Universidad de GranadaBracciali, Cleonice F. [UNESP]Piñar, Miguel A.2023-07-29T13:26:56Z2023-07-29T13:26:56Z2023-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article183-206http://dx.doi.org/10.1007/s11075-022-01434-4Numerical Algorithms, v. 92, n. 1, p. 183-206, 2023.1572-92651017-1398http://hdl.handle.net/11449/24782810.1007/s11075-022-01434-42-s2.0-85141170199Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNumerical Algorithmsinfo:eu-repo/semantics/openAccess2023-07-29T13:26:56Zoai:repositorio.unesp.br:11449/247828Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:44:14.749617Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
On multivariate orthogonal polynomials and elementary symmetric functions |
title |
On multivariate orthogonal polynomials and elementary symmetric functions |
spellingShingle |
On multivariate orthogonal polynomials and elementary symmetric functions On multivariate orthogonal polynomials and elementary symmetric functions Bracciali, Cleonice F. [UNESP] Elementary symmetric functions Multivariate orthogonal polynomials Symmetric polynomials Bracciali, Cleonice F. [UNESP] Elementary symmetric functions Multivariate orthogonal polynomials Symmetric polynomials |
title_short |
On multivariate orthogonal polynomials and elementary symmetric functions |
title_full |
On multivariate orthogonal polynomials and elementary symmetric functions |
title_fullStr |
On multivariate orthogonal polynomials and elementary symmetric functions On multivariate orthogonal polynomials and elementary symmetric functions |
title_full_unstemmed |
On multivariate orthogonal polynomials and elementary symmetric functions On multivariate orthogonal polynomials and elementary symmetric functions |
title_sort |
On multivariate orthogonal polynomials and elementary symmetric functions |
author |
Bracciali, Cleonice F. [UNESP] |
author_facet |
Bracciali, Cleonice F. [UNESP] Bracciali, Cleonice F. [UNESP] Piñar, Miguel A. Piñar, Miguel A. |
author_role |
author |
author2 |
Piñar, Miguel A. |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Facultad de Ciencias. Universidad de Granada |
dc.contributor.author.fl_str_mv |
Bracciali, Cleonice F. [UNESP] Piñar, Miguel A. |
dc.subject.por.fl_str_mv |
Elementary symmetric functions Multivariate orthogonal polynomials Symmetric polynomials |
topic |
Elementary symmetric functions Multivariate orthogonal polynomials Symmetric polynomials |
description |
We 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. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-29T13:26:56Z 2023-07-29T13:26:56Z 2023-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s11075-022-01434-4 Numerical Algorithms, v. 92, n. 1, p. 183-206, 2023. 1572-9265 1017-1398 http://hdl.handle.net/11449/247828 10.1007/s11075-022-01434-4 2-s2.0-85141170199 |
url |
http://dx.doi.org/10.1007/s11075-022-01434-4 http://hdl.handle.net/11449/247828 |
identifier_str_mv |
Numerical Algorithms, v. 92, n. 1, p. 183-206, 2023. 1572-9265 1017-1398 10.1007/s11075-022-01434-4 2-s2.0-85141170199 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Numerical Algorithms |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
183-206 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1822218595152691200 |
dc.identifier.doi.none.fl_str_mv |
10.1007/s11075-022-01434-4 |