Charles Fefferman, Interpolation of C^m Functions in n dimensions

Fix positive integers m,n. Given points x1,...,xN in R^n, and given
real numbers y1,...,yN, we compute efficiently a function F in C^m
(R^n),such that F(xk)=yk for each k, with the C^m norm of F having
the least possible order of magnitude.
We consider also several variants of the above problem.
(Joint work with Bo'az Klartag.)