Abstract
If F ⊂ ℝ is a closed set such that the space of all Whitney jets on F admits an extension operator then there exists such an extension operator whose values are holomorphic in ℂF if and only if ∂F is compact. In the case F is a compact set, there is even an extension operatorfor which the extensions are holomorphic in (ℂ ∪ {∞})F.
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Boonen, C., Frerick, L. Extension Operators with Analytic Values. Results. Math. 44, 242–257 (2003). https://doi.org/10.1007/BF03322985
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DOI: https://doi.org/10.1007/BF03322985