GCOEレクチャーズ

2010年01月27日(水)

14:40-16:10   数理科学研究科棟(駒場) 002号室
Charles Fefferman 氏 (Princeton University)
Extension of Functions and Interpolation of Data
[ 講演概要 ]
This series of three lectures will discuss the following questions. No special background will be assumed, and the third lecture will not assume familiarity with the first two.

Fix positive integers $m, n$. Let $f$ be a real-valued function on a subset $E$ of $\\mathbf{R}^n$. How can we tell whether $f$ extends to a $C^m$ function $F$ on the whole $\\mathbf{R}^n$?
If $F$ exists, how small can we take its $C^m$ norm? Can we take $F$ to depend linearly on $f$? What can we say about the derivatives of $F$ at a given point of $E$?

Suppose $E$ is finite. Can we then compute an $F$ with $C^m$ norm close to least-possible? How many operations does it take? What if we ask merely that $F$ and $f$ agree approximately on $E$? What if we are allowed to delete a few points of $E$?

What can be said about the above problems for function spaces other than $C^m(\\mathbf{R}^n)$?