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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Whitney's extension problems and interpolation of data


Author: Charles Fefferman
Journal: Bull. Amer. Math. Soc. 46 (2009), 207-220
MSC (2000): Primary 49K24, 52A35
Published electronically: November 24, 2008
MathSciNet review: 2476412
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Abstract | References | Similar Articles | Additional Information

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: http://dx.doi.org/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
Published electronically: November 24, 2008
Additional Notes: The author was supported by grants DMS-0601025 and ONR-N00014-08-1-0678.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.