School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Princeton University

Let X be a Banach space of continuous functions on R^n, and let f:E->R be a function defined

Abstract:

on an (arbitrary) given subset E of R^n. How can we tell whether f extends to a function F \in X ?

If such an F exists, then how small can we take its norm? What can we say about its derivatives at a given point?

Can we take F to depend linearly on f?

Suppose E is finite. Can we compute an F as above whose norm has the smallest possible order of magnitude?

How many computer operations does it take?

The talk explains what we know about these questions for X=C^m(R^n), X=C^m, alpha(R^n) (m-th derivatives in

Lip(alpha)) and X=W^m,p(R^n). Some of the main results are joint work with Arie Israel, Kevin Luli, and Bo'az Klartag.

Coffee will be served at 12:00 before the lecture

at Schreiber building 006