# Whitney’s extension problem for $C^m$

### Abstract

Let $f$ be a real-valued function on a compact set in $\mathbb{R}^n$, and let $m$ be a positive integer. We show how to decide whether $f$ extends to a $\mathbb{C}^m$ function on $\mathbb{R}^n$.

## Authors

Charles Fefferman

Department of Mathematics, Princeton University, Princeton, NJ 08544, United States