Necessary Conditions for Interpolation by Multivariate Polynomials

Abstract Let $$\Omega $$ Ω be a smooth, bounded, convex domain in $${\mathbb {R}}^n$$ R n and let $$\Lambda _k$$ Λ k finite subset of . We find necessary geometric conditions for to interpolating the space multivariate polynomials degree at most k Our results are asymptotic The density obtained match precisely that sampling sets known satisfy expressed terms equilibrium potential set. Moreover we prove particular case unit ball, large enough, there no bases orthogonal reproducing kernels