Whitney's interpolation problem and interpolation I and II
by
Charles Fefferman
Princeton University

Fix positive integers m,   n. Let f:E→ R be given, with E an arbitrary given subset of Rⁿ. How can we decide whether f extends to a C^m function F on the whole Rⁿ? If F exists, how small can we take its C^m norm? What can we say about the derivatives of F at a given point? Can we take F to depend linearly on f? What if we require only that F agree approximately with f on E? Suppose E is finite. Can we compute an F whose C^m norm is close to smallest possible? How many computer operations does it take? What if we are allowed to delete a few points from E? The first talk states results, the second talk gives some ideas from the proofs. Many of the results are joint work with Bo'az Klartag.

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Date received: January 25, 2008