On interpolation by radial polynomials

A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (his Lemma 3.1). (1) Lemma. If ∑n i=1 cip(xi) = 0 for all p ∈ Π<k(IR ), then (−1) n ∑