School of Mathematical Sciences
Monday, December 13, 2010
Schreiber 006, 12:15
Technion, Israel Institute of Technology
The Whitney problem: how to measure
smoothness of functions
on finite sets
In 1934 H. Whitney posed the following problem: Let f be a function
defined on a closed subset E of R^n. How can we tell whether f
extends to a C^m-smooth function defined on all of R^n?
We discuss different aspects of this classical problem including its
interesting connections with Convex Geometry (Helly's theorem),
Lipschitz selections of set-valued functions and Analysis on
The main part of the talk will address the "finiteness
principle" which states that the Whitney extension problem can be
reduced to the same kind of the problem, but for finite sets with
prescribed number of points.
We will present several constructive criteria for restrictions of
C^2-functions and Sobolev W^1_p and W^2_p-functions to
arbitrary closed subsets of R^2.
No special background is necessary.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006