Wednesday, March 7 – 3:30 pm — Room 380W
Fitting smooth functions to data:
Let X be our favorite Banach space of continuous functions on R^n. Given a function f defined on some given subset of R^n, how can we decide whether f extends to a function F on all of R^n, belonging to the space X? If such an F exists, then how small can we take its norm?
What can we say about the derivatives of F at a given point? Can we take F to depend linearly on f?
Suppose E is a large finite set. Can we compute an F as above with norm having the least possible order of magnitude? How many computer operations does it take? What if we require only that F agree with f to a given accuracy, rather than demanding perfect agreement? What if we are allowed to discard a few data points as “outliers”? Which data points should we discard?
Joint work with Arie Israel, Bo’az Klartag, Kevin Luli and Pavel Shvartsman.
DetailsThe Mathematics Research Center Distinguished Lecture Series Presents: Charles Fefferman (Princeton University)
Charles Fefferman (Princeton University)
March 7, 2018
3:30 AM - 4:30 PM