## Whitney’s extension problems and interpolation of data

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- by Charles Fefferman PDF
- 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).## References

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*Higher-order tangents and Fefferman’s paper on Whitney’s extension problem*, Annals of Math., (to appear).

*Whitney’s extension problem in certain function spaces*, (preprint).

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*The $C^m$ norm of a function with prescribed jets II*, (to appear). [19]19 C. Fefferman and B. Klartag,

*Fitting a $C^m$-smooth function to data I*, Annals of Math., (accepted (2006)). [20]20 C. Fefferman and B. Klartag,

*Fitting a $C^m$-smooth function to data II*, Revista Matemática Iberoamericana, (accepted (2007)). [21]21 C. Fefferman and B. Klartag,

*An example related to Whitney extension with almost minimal $C^m$ norm*, (to appear). [22]22 C. Fefferman,

*Fitting a $C^m$-smooth function to data III*, Annals of Math., (accepted (2007)).

*Sobolev $W^1_p$-spaces on closed sets and domains in ${\mathbb {R}}^n$*, (to appear).

## 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
- 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.
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2476412