School of Mathematical Sciences
Monday, May 20, 2013
Schreiber 006, 12:15
Extension and interpolation problems I.
Abstract: Let X be a Banach space of continuous functions on R^n, and let f:E->R be a function defined
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