Extension operators for smooth functions on compact subsets of the reals

Abstract

We introduce sufficient as well as necessary conditions for a compact set $K$ such that there is a continuous linear extension operator from the space of restrictions $C^{\infty }(K)=\{F{|}_K:F\in C^{\infty }(\mathbb{R})\}$ to $C^{\infty }(\mathbb{R})$. This allows us to deal with examples of the form $K=\{a_n:n\in \mathbb{N}\}\cup \{0\}$ for $a_n\to 0$ previously considered by Fefferman and Ricci as well as Vogt.

18 pages