Interpolation at a few points

For k=2 and 3, B. Shekhtman proved that n + k-1 is the smallest dimension of a subspace, F subset of or equal to C(R(n)) that can interpolate to k specified real values at k distinct points in R(n). Here we characterize such spaces that interpolate at a few points. The characterization provides an economical proof of Shekhtman's theorems, as well as establishing new properties of these spaces. (C) 1999 Academic Press.