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 \(a_n\rightarrow 0\) previously considered by Fefferman and Ricci as well as Vogt.
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Acknowledgements
The research of all authors was partially supported by GVA AICO/2016/054 . The research of the second author was partially supported by the project MTM2016-76647-P.
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Frerick, L., Jordá, E. & Wengenroth, J. Extension operators for smooth functions on compact subsets of the reals. Math. Z. 295, 1537–1552 (2020). https://doi.org/10.1007/s00209-019-02388-5
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DOI: https://doi.org/10.1007/s00209-019-02388-5