Extension operators for smooth functions on compact subsets of the reals

2016/11/21 by Frerick, Leonhard, Jorda, Enrique, Wengenroth, Jochen
#46A63 #46E25 #47A57 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1611.06808

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^∞(K)=\lbrace F|_K: F∈ C^∞(\mathbb R)\rbrace to C^∞(\mathbb R). This allows us to deal with examples of the form K=\lbrace a_n:n∈\mathbb N\rbrace ∪ \lbrace 0\rbrace for a_n→ 0 previously considered by Fefferman and Ricci as well as Vogt.

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