Polynomial interpolation in \(R_{3}\) (Q1776486)

A linear subspace \({G\subset C(R_n)}\) is called \(k\)-interpolating if for every choice of distinct points \({u_1,u_2,\dots,u_k\in R_n}\) and for any choice of scalars \({a_1,a_2,\dots,a_k\in R}\), there exists \({g\in G}\) such that \({g(u_j)=a_j}\), for \({j=1,2,\dots,k}\). The main result of the article is the example of a 12-dimensional subspace \({G\subset C(R_3)}\) which is 4-interpolating.