American Institute of Mathematics, Palo Alto, California
Charles Fefferman and Nahum Zobin
A lot is known about whether a given function $f$ on a large finite subset $E \subset \R^n$ extends to a $C^m$ \ function on the whole of $\R^n$ with small norm.
For instance, suppose $f : E \to \R$, where $E$ is an arbitrarily large finite subset of the plane. Assume that the restriction of $f$ to any six points of $E$ can be extended to the whole plane with $C^2$ norm less than 1. Then $f$ can be extended to the whole plane with $C^2$ norm less than a universal constant.
The analogous results for Sobolev norms are at a much earlier stage. We would like to make further progress on these (and related) problems, and to explore whether there is a sensible version of these questions for finite sets not necessarily contained in $\R^n$.
The workshop schedule.
A report on the workshop activities.