Whitney’s extension problems and interpolation of data

Fefferman, Charles

doi:10.1090/S0273-0979-08-01240-8

Whitney’s extension problems and interpolation of data
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Bull. Amer. Math. Soc. 46 (2009), 207-220 Request permission

Abstract:

Given a function $f: E \rightarrow {\mathbb {R}}$ with $E \subset {\mathbb {R}}^n$, we explain how to decide whether $f$ extends to a $C^m$ function $F$ on ${\mathbb {R}}^n$. If $E$ is finite, then one can efficiently compute an $F$ as above, whose $C^m$ norm has the least possible order of magnitude (joint work with B. Klartag).

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