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Title: A coordinate-free proof of the finiteness principle for Whitney’s extension problem
We present a coordinate-free version of Fefferman’s solution of Whitney’s extension problem in the space Cm−1,1(Rn). While the original argument relies on an elaborate induction on collections of partial derivatives, our proof uses the language of ideals and translation-invariant subspaces in the ring of polynomials. We emphasize the role of compactness in the proof, first in the familiar sense of topological compactness, but also in the sense of finiteness theorems arising in logic and semialgebraic geometry. These techniques may be relevant to the study of Whitney-type extension problems on sub-Riemannian manifolds where global coordinates are generally unavailable.  more » « less
Award ID(s):
1700404
PAR ID:
10170420
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Revista Matemática Iberoamericana
ISSN:
0213-2230
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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