Interpolation and Extension of Functions
Interpolation and Extension of Functions
-
Charles Fefferman, Princeton University
What's Happening in Fine Hall
Zoom link:听
Passcode:听803011
Let X be your favorite Banach space of continuous functions on R^n.听Given a function f:E->R defined on a (possibly awful) subset E in R^n,听how can we tell whether f extends to a function F:R^n->R belonging to听X? If such an F exists, then how small can we take its norm? What can听we say about the derivatives听 of F at or near points of E? Can we take听F to depend linearly on f?听Suppose E is finite. Can we compute an F as above? How听many computer听operations does it take? What if F is allowed to agree only听approximately with f ? What if we are allowed to discard a few points听of E as "outliers"? Which听 points should we discard?