The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball
We consider a family of orthogonal polynomials in several variables with respect to a Sobolev-type inner product, obtained from adding a gradient operator of order j, evaluated in a fixed point to a standard inner product. We study explicit relations between the Sobolev-type polynomials and the stand...
- Autores:
-
Dueñas, Herbert
Gómez, Wilmer M.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2015
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/61895
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/61895
http://bdigital.unal.edu.co/60707/
- Palabra clave:
- 51 Matemáticas / Mathematics
Orthogonal polynomials in several variables
Asymptotics behavior
Sobolev inner products.
Polinomios ortogonales en varias variables
comportamiento asintótico
producto interno de tipo Sobolev
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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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_abf2Dueñas, Herbert16b3ae7e-c0a9-45ed-91dd-eeca48580be0300Gómez, Wilmer M.aabc88c7-9545-4bdc-a659-4a8c154d56723002019-07-02T20:47:04Z2019-07-02T20:47:04Z2015-01-01ISSN: 2357-6529https://repositorio.unal.edu.co/handle/unal/61895http://bdigital.unal.edu.co/60707/We consider a family of orthogonal polynomials in several variables with respect to a Sobolev-type inner product, obtained from adding a gradient operator of order j, evaluated in a fixed point to a standard inner product. We study explicit relations between the Sobolev-type polynomials and the standard polynomials, among the kernel functions associated to the Sobolev-type polynomials and the kernel functions associated to the standard polynomials. In addition, an example for a particular choice of a classical measure σ ∈ Rd is analyzed. Finally, we obtain the asymptotics of the some derivatives of the kernel functions evaluated in some points of the unit ball in d variables.Consideramos una familia de polinomios ortogonales en varias variables con respecto a un producto interno de tipo Sobolev, el cual se obtiene al adicionar a un producto interno estándar un operador gradiente de orden j, evaluado en un punto fijo. Estudiamos relaciones entre los polinomios de tipo Sobolev y los polinomios estándar, como relaciones entre el núcleo asociado a los polinomios de tipo Sobolev y el núcleo de los polinomios estándar. Adicionalmente, estudiamos un caso particular de una medida σ ∈ Rd Finalmente, se obtienen los comportamientos asintóticos de las derivadas del núcleo evaluadas en puntos de la bola unidad en d variables.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticashttps://revistas.unal.edu.co/index.php/bolma/article/view/51845Universidad Nacional de Colombia Revistas electrónicas UN Boletín de MatemáticasBoletín de MatemáticasDueñas, Herbert and Gómez, Wilmer M. (2015) The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball. Boletín de Matemáticas, 22 (1). pp. 39-53. ISSN 2357-652951 Matemáticas / MathematicsOrthogonal polynomials in several variablesAsymptotics behaviorSobolev inner products.Polinomios ortogonales en varias variablescomportamiento asintóticoproducto interno de tipo SobolevThe asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ballArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL51845-252716-1-SM.pdfapplication/pdf440868https://repositorio.unal.edu.co/bitstream/unal/61895/1/51845-252716-1-SM.pdf606a81b2c1f5cefd7b0640f5150774eaMD51THUMBNAIL51845-252716-1-SM.pdf.jpg51845-252716-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5784https://repositorio.unal.edu.co/bitstream/unal/61895/2/51845-252716-1-SM.pdf.jpg7aa689f5d608b58c257ac4045d664bb8MD52unal/61895oai:repositorio.unal.edu.co:unal/618952024-04-20 23:26:19.193Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| title |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| spellingShingle |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball 51 Matemáticas / Mathematics Orthogonal polynomials in several variables Asymptotics behavior Sobolev inner products. Polinomios ortogonales en varias variables comportamiento asintótico producto interno de tipo Sobolev |
| title_short |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| title_full |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| title_fullStr |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| title_full_unstemmed |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| title_sort |
The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball |
| dc.creator.fl_str_mv |
Dueñas, Herbert Gómez, Wilmer M. |
| dc.contributor.author.spa.fl_str_mv |
Dueñas, Herbert Gómez, Wilmer M. |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics Orthogonal polynomials in several variables Asymptotics behavior Sobolev inner products. Polinomios ortogonales en varias variables comportamiento asintótico producto interno de tipo Sobolev |
| dc.subject.proposal.spa.fl_str_mv |
Orthogonal polynomials in several variables Asymptotics behavior Sobolev inner products. Polinomios ortogonales en varias variables comportamiento asintótico producto interno de tipo Sobolev |
| description |
We consider a family of orthogonal polynomials in several variables with respect to a Sobolev-type inner product, obtained from adding a gradient operator of order j, evaluated in a fixed point to a standard inner product. We study explicit relations between the Sobolev-type polynomials and the standard polynomials, among the kernel functions associated to the Sobolev-type polynomials and the kernel functions associated to the standard polynomials. In addition, an example for a particular choice of a classical measure σ ∈ Rd is analyzed. Finally, we obtain the asymptotics of the some derivatives of the kernel functions evaluated in some points of the unit ball in d variables. |
| publishDate |
2015 |
| dc.date.issued.spa.fl_str_mv |
2015-01-01 |
| dc.date.accessioned.spa.fl_str_mv |
2019-07-02T20:47:04Z |
| dc.date.available.spa.fl_str_mv |
2019-07-02T20:47:04Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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http://purl.org/coar/resource_type/c_6501 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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Text |
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http://purl.org/redcol/resource_type/ART |
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http://purl.org/coar/resource_type/c_6501 |
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publishedVersion |
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ISSN: 2357-6529 |
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https://repositorio.unal.edu.co/handle/unal/61895 |
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http://bdigital.unal.edu.co/60707/ |
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ISSN: 2357-6529 |
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https://repositorio.unal.edu.co/handle/unal/61895 http://bdigital.unal.edu.co/60707/ |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/bolma/article/view/51845 |
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Universidad Nacional de Colombia Revistas electrónicas UN Boletín de Matemáticas Boletín de Matemáticas |
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Dueñas, Herbert and Gómez, Wilmer M. (2015) The asymptotics of the kernel functions associated to orthogonal polynomials in several variables on the unit ball. Boletín de Matemáticas, 22 (1). pp. 39-53. ISSN 2357-6529 |
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Derechos reservados - Universidad Nacional de Colombia |
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http://purl.org/coar/access_right/c_abf2 |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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info:eu-repo/semantics/openAccess |
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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 |
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Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas |
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