Whitney [Wh2] proved that a function defined on a closed subset of $\mathbb{R}$ is the restriction of a $\mathcal{C}^m$ function if the limiting values of all $m^{\rm th}$ divided differences form a continuous function. We show that Fefferman’s solution of Whitney’s problem for $\mathbb{R}^n$ [F, Th. 1] is equivalent to a variant of our conjecture in [BMP2] giving a criterion for $\mathcal{C}^m$ extension in terms of iterated limits of finite differences.
Edward Bierstone 1 ; Pierre D. Milman 1 ; Wiesław Pawłucki 2
@article{10_4007_annals_2006_164_361,
author = {Edward Bierstone and Pierre D. Milman and Wies{\l}aw Paw{\l}ucki},
title = {Higher-order tangents and {Fefferman{\textquoteright}s} paper on {Whitney{\textquoteright}s} extension problem},
journal = {Annals of mathematics},
pages = {361--370},
year = {2006},
volume = {164},
number = {1},
doi = {10.4007/annals.2006.164.361},
mrnumber = {2233851},
zbl = {1109.58015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.361/}
}
TY - JOUR AU - Edward Bierstone AU - Pierre D. Milman AU - Wiesław Pawłucki TI - Higher-order tangents and Fefferman’s paper on Whitney’s extension problem JO - Annals of mathematics PY - 2006 SP - 361 EP - 370 VL - 164 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.361/ DO - 10.4007/annals.2006.164.361 LA - en ID - 10_4007_annals_2006_164_361 ER -
%0 Journal Article %A Edward Bierstone %A Pierre D. Milman %A Wiesław Pawłucki %T Higher-order tangents and Fefferman’s paper on Whitney’s extension problem %J Annals of mathematics %D 2006 %P 361-370 %V 164 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.361/ %R 10.4007/annals.2006.164.361 %G en %F 10_4007_annals_2006_164_361
Edward Bierstone; Pierre D. Milman; Wiesław Pawłucki. Higher-order tangents and Fefferman’s paper on Whitney’s extension problem. Annals of mathematics, Tome 164 (2006) no. 1, pp. 361-370. doi: 10.4007/annals.2006.164.361
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