## UNIVERSITY OF PENNSYLVANIA

## Department of Mathematics

Fall 2008 -Hans Rademacher Lectures in Mathematics

Charles Fefferman

## Department of Mathematics

Princeton University

will speak on

## Extension and Interpolation of Functions

The infinite flavor

Suppose we are given a real-valued function f, defined on an (arbitrary) given subset of R^{n}. How can we tell whether f extends to a C^{m}function F on the whole R^{n}? If F exists, then 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?

The finite flavor(joint work with Bo'az Klartag)

Suppose we are given a real-valued function f defined on a finite set E in R^{n}. How can we compute a C^{m}function F that agrees with f on E and has C^{m}norm (nearly) as small as possible? How many computer operations does it take? How small is the C^{m}norm of such an F? What if we demand that F agree with f only approximately? What if we are allowed to delete a few points of E?

Monday....November 10, 2008.....4:00pm

Tuesday....November 11, 2008....4:00pm

Wednesday....November 12, 2008....4:00pm

Thursday....November 13, 2008....4:00pm

Lectures will be held in A6 of the David Rittenhouse Laboratory,

S.E. corner of 33rd and Walnut Streets, Philadelphia, PA.

Tea: 4E17 DRL at 3:30pm.

For further information, please call the Department of Mathematics at the University of Pennsylvania - 215-898-8627.