Document type
ArticleVersion
Accepted versionPublication date
All rights reserved
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/179888
Necessary Conditions for Interpolation by Multivariate Polynomials
Journal Title
Director/Tutor
Journal ISSN
Volume Title
Related resource
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 $k$.
Subject (English)
Citation
Citation
ANTEZANA, Jorge, MARZO SÁNCHEZ, Jordi and ORTEGA CERDÀ, Joaquim. Necessary Conditions for Interpolation by Multivariate Polynomials. Computational Methods And Function Theory. 2021. ISSN 1617-9447. [consulted: 13 of June of 2026]. Available at: https://hdl.handle.net/2445/179888