Necessary Conditions for Interpolation by Multivariate Polynomials

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 ne...

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Autores principales: Antezana, Jorge Abel, Marzo, Jordi, Ortega Cerdà, Joaquim
Formato: Articulo
Lenguaje:Inglés
Publicado: 2021
Materias:
Matemática
Ciencias Exactas
Interpolating sequences
Multivariate polynomials
Reproducing kernels
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/140442
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-140442
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Ciencias Exactas
Interpolating sequences
Multivariate polynomials
Reproducing kernels
spellingShingle Matemática
Ciencias Exactas
Interpolating sequences
Multivariate polynomials
Reproducing kernels
Antezana, Jorge Abel
Marzo, Jordi
Ortega Cerdà, Joaquim
Necessary Conditions for Interpolation by Multivariate Polynomials
topic_facet Matemática
Ciencias Exactas
Interpolating sequences
Multivariate polynomials
Reproducing kernels
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.
format Articulo
Articulo
author Antezana, Jorge Abel
Marzo, Jordi
Ortega Cerdà, Joaquim
author_facet Antezana, Jorge Abel
Marzo, Jordi
Ortega Cerdà, Joaquim
author_sort Antezana, Jorge Abel
title Necessary Conditions for Interpolation by Multivariate Polynomials
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
publishDate 2021
url http://sedici.unlp.edu.ar/handle/10915/140442
work_keys_str_mv AT antezanajorgeabel necessaryconditionsforinterpolationbymultivariatepolynomials
AT marzojordi necessaryconditionsforinterpolationbymultivariatepolynomials
AT ortegacerdajoaquim necessaryconditionsforinterpolationbymultivariatepolynomials
bdutipo_str Repositorios
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