Mathematics Colloquium

Tel Aviv University

Thursday, June 8, 2017
Schreiber 006
:: 2017 Mathematics Wolf Prize Lecture ::
Charles Fefferman
Princeton University
Interpolation and Approximation of Data by Smooth Functions

The talk will present results with Bo'az Klartag, Arie Israel, Garving (Kevin) Luli and Pavel Shvartsman on the following questions, which have fascinated me for the last 15 years.

Let X be our favorite Banach space of continuous functions on ℝn, and let f be a real-valued function on an (arbitrary) given subset E of ℝn. How can we tell whether f extends to a function F in X? If such an F exists, how small can we take its norm? Can we take F to depend linearly on f? What can we say about the derivatives of F at a given point?

Suppose E is finite. Can we compute such an F with close-to-minimal norm in X? How many computer operations does it take? What if F is required to agree only approximately with f on E? What if we are allowed to discard a few "outliers" from E to reduce the norm of F; which points should we discard? What changes if f and F are vector-valued?

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