Interpolating Subspaces in R _N

Abstract

A k-interpolating subspace of C(R _n ) is a subspace F ⊂ C(R _n ) such that for every choice of distinct points t ₁,..., t _k ∊ R _n and every choice of scalars α ₁,..., α _k ∈ R there exists f ∈ F with f(t _j ) = α _j , j = 1,..., k.

We prove that

$$\min \left\{ {\dim F:F \subset C({R_n})isK - \operatorname{int} erpolating} \right\} = n + k - 1$$

for k = 2, 3.