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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
DOI: https://doi.org/10.1090/S0273-0979-08-01240-8
Published electronically: November 24, 2008
MathSciNet review: 2476412
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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
MR Author ID: 65640
Email: cf@math.princeton.edu

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.