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 in Rn extends to a Cm function on the whole of Rn with small norm.
For instance, suppose f : E → 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 C2 norm less than 1. Then f can be extended to the whole plane with C2 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 Rn.
The workshop schedule.
A report on the workshop activities.