Favard interpolation from subsets of a rectangular lattice

This is a study of Favard interpolation–in which the nnth derivatives of the interpolant are bounded above by a constant times the nnth divided differences of the data–in the case where the data are given on some subset of a rectangular lattice in RkRk. In some instances, depending on the geometry of this subset, we construct a Favard interpolant, and in other instances, we prove that none exists.