On extending C^k functions from an open set to R, with applications

W. D. Burgess, R. Raphael

For $k\in \mathbb{N}\cup \{\infty \}$ and $U$ open in $\mathbb{R}$, let $\C^{\,k}(U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown for $f\in \…