Necessary Conditions for Interpolation by Multivariate Polynomials
- Autores
- Antezana, Jorge Abel; Marzo, Jordi; Ortega Cerdà, Joaquim
- Año de publicación
- 2021
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let Ω be a smooth, bounded, convex domain in Rn and let Λk be a finite subset of Ω. We find necessary geometric conditions for Λk to be interpolating for the space of multivariate polynomials of degree at most k. Our results are asymptotic in k. The density conditions obtained match precisely the necessary geometric conditions that sampling sets are known to satisfy and are expressed in terms of the equilibrium potential of the convex set. Moreover we prove that in the particular case of the unit ball, for k large enough, there are no bases of orthogonal reproducing kernels in the space of polynomials of degree at most k.
Facultad de Ciencias Exactas - Materia
-
Matemática
Ciencias Exactas
Interpolating sequences
Multivariate polynomials
Reproducing kernels - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/140442
Ver los metadatos del registro completo
| id |
SEDICI_d040dff7eacd59804164245b26e5feae |
|---|---|
| oai_identifier_str |
oai:sedici.unlp.edu.ar:10915/140442 |
| network_acronym_str |
SEDICI |
| repository_id_str |
1329 |
| network_name_str |
SEDICI (UNLP) |
| spelling |
Necessary Conditions for Interpolation by Multivariate PolynomialsAntezana, Jorge AbelMarzo, JordiOrtega Cerdà, JoaquimMatemáticaCiencias ExactasInterpolating sequencesMultivariate polynomialsReproducing kernelsLet Ω be a smooth, bounded, convex domain in Rn and let Λk be a finite subset of Ω. We find necessary geometric conditions for Λk to be interpolating for the space of multivariate polynomials of degree at most k. Our results are asymptotic in k. The density conditions obtained match precisely the necessary geometric conditions that sampling sets are known to satisfy and are expressed in terms of the equilibrium potential of the convex set. Moreover we prove that in the particular case of the unit ball, for k large enough, there are no bases of orthogonal reproducing kernels in the space of polynomials of degree at most k.Facultad de Ciencias Exactas2021-08-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1-19http://sedici.unlp.edu.ar/handle/10915/140442enginfo:eu-repo/semantics/altIdentifier/issn/1617-9447info:eu-repo/semantics/altIdentifier/issn/2195-3724info:eu-repo/semantics/altIdentifier/doi/10.1007/s40315-021-00410-8info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:23:59Zoai:sedici.unlp.edu.ar:10915/140442Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:23:59.376SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| title |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| spellingShingle |
Necessary Conditions for Interpolation by Multivariate Polynomials Antezana, Jorge Abel Matemática Ciencias Exactas Interpolating sequences Multivariate polynomials Reproducing kernels |
| title_short |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| title_full |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| title_fullStr |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| title_full_unstemmed |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| title_sort |
Necessary Conditions for Interpolation by Multivariate Polynomials |
| dc.creator.none.fl_str_mv |
Antezana, Jorge Abel Marzo, Jordi Ortega Cerdà, Joaquim |
| author |
Antezana, Jorge Abel |
| author_facet |
Antezana, Jorge Abel Marzo, Jordi Ortega Cerdà, Joaquim |
| author_role |
author |
| author2 |
Marzo, Jordi Ortega Cerdà, Joaquim |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
Matemática Ciencias Exactas Interpolating sequences Multivariate polynomials Reproducing kernels |
| topic |
Matemática Ciencias Exactas Interpolating sequences Multivariate polynomials Reproducing kernels |
| dc.description.none.fl_txt_mv |
Let Ω be a smooth, bounded, convex domain in Rn and let Λk be a finite subset of Ω. We find necessary geometric conditions for Λk to be interpolating for the space of multivariate polynomials of degree at most k. Our results are asymptotic in k. The density conditions obtained match precisely the necessary geometric conditions that sampling sets are known to satisfy and are expressed in terms of the equilibrium potential of the convex set. Moreover we prove that in the particular case of the unit ball, for k large enough, there are no bases of orthogonal reproducing kernels in the space of polynomials of degree at most k. Facultad de Ciencias Exactas |
| description |
Let Ω be a smooth, bounded, convex domain in Rn and let Λk be a finite subset of Ω. We find necessary geometric conditions for Λk to be interpolating for the space of multivariate polynomials of degree at most k. Our results are asymptotic in k. The density conditions obtained match precisely the necessary geometric conditions that sampling sets are known to satisfy and are expressed in terms of the equilibrium potential of the convex set. Moreover we prove that in the particular case of the unit ball, for k large enough, there are no bases of orthogonal reproducing kernels in the space of polynomials of degree at most k. |
| publishDate |
2021 |
| dc.date.none.fl_str_mv |
2021-08-30 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://sedici.unlp.edu.ar/handle/10915/140442 |
| url |
http://sedici.unlp.edu.ar/handle/10915/140442 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/issn/1617-9447 info:eu-repo/semantics/altIdentifier/issn/2195-3724 info:eu-repo/semantics/altIdentifier/doi/10.1007/s40315-021-00410-8 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) |
| dc.format.none.fl_str_mv |
application/pdf 1-19 |
| dc.source.none.fl_str_mv |
reponame:SEDICI (UNLP) instname:Universidad Nacional de La Plata instacron:UNLP |
| reponame_str |
SEDICI (UNLP) |
| collection |
SEDICI (UNLP) |
| instname_str |
Universidad Nacional de La Plata |
| instacron_str |
UNLP |
| institution |
UNLP |
| repository.name.fl_str_mv |
SEDICI (UNLP) - Universidad Nacional de La Plata |
| repository.mail.fl_str_mv |
alira@sedici.unlp.edu.ar |
| _version_ |
1846064294193528832 |
| score |
13.22299 |