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Whitney's extension problems and interpolation of data

Author(s): Charles Fefferman
Journal: Bull. Amer. Math. Soc. 46 (2009), 207-220.
MSC (2000): Primary 49K24, 52A35
Posted: November 24, 2008
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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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Additional Information:

Charles Fefferman
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544
Email: cf@math.princeton.edu

DOI: 10.1090/S0273-0979-08-01240-8
PII: S 0273-0979(08)01240-8
Keywords: Whitney extension problem, interpolation
Received by editor(s): September 2, 2008
Posted: November 24, 2008
Additional Notes: The author was supported by grants DMS-0601025 and ONR-N00014-08-1-0678.
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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