Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/179888
Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Antezana, Jorge | - |
dc.contributor.author | Marzo Sánchez, Jordi | - |
dc.contributor.author | Ortega Cerdà, Joaquim | - |
dc.date.accessioned | 2021-09-08T09:36:21Z | - |
dc.date.available | 2022-08-30T05:10:19Z | - |
dc.date.issued | 2021-08-30 | - |
dc.identifier.issn | 1617-9447 | - |
dc.identifier.uri | http://hdl.handle.net/2445/179888 | - |
dc.description.abstract | Let $\Omega$ be a smooth, bounded, convex domain in $\mathbb R^n$ and let $\Lambda_k$ be a finite subset of $\Omega$. We find necessary geometric conditions for $\Lambda_k$ 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 they 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 $k$. | - |
dc.format.extent | 19 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Verlag | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s40315-021-00410-8 | - |
dc.relation.ispartof | Computational Methods And Function Theory, 2021 | - |
dc.relation.uri | https://doi.org/10.1007/s40315-021-00410-8 | - |
dc.rights | (c) Springer Verlag, 2021 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Anàlisi harmònica | - |
dc.subject.classification | Teoria de l'aproximació | - |
dc.subject.other | Harmonic analysis | - |
dc.subject.other | Approximation theory | - |
dc.title | Necessary Conditions for Interpolation by Multivariate Polynomials | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 713790 | - |
dc.date.updated | 2021-09-08T09:36:21Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
713790.pdf | 352.21 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.