CRM: Centro De Giorgi
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Euclidean Harmonic Analysis, Nilpotent Lie Groups and PDEs

Extension of Functions and Interpolation of Data (Colloquio de Giorgi)

speaker: Charles Fefferman (Princeton University)

abstract: How can we tell whether a given real-valued function f on an arbitrary given subset of Rn extends to a Cm function F on the whole Rn? If F exists, how small can we take its Cm norm? What can we say about the derivatives of F at a given point? Can we make F depend linearly on f? Suppose f is defined only on a finite set. How can we compute an extension F with close-to-minimal norm? How many computer operations does it take? What if F is required merely to agree approximately with f? What if we are allowed to discard a few of the points of E? What about function spaces other than Cm? Many of the results discussed are joint work with Bo'az Klartag.

Mon 19 Apr, 15:00 - 17:00, Sala Stemmi
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