Geodesic
Higher-order tangents and Fefferman’s paper on Whitney’s extension problem
Edward Bierstone1 ; Pierre D. Milman1 ; Wiesław Pawłucki2
1 Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
2 Institute of Mathematics, Jagiellonian University, 30-348 Kraków, Poland
Annals of mathematics, Tome 164 (2006) no. 1, pp. 361-370.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2006.164.361

Edward Bierstone 1 ; Pierre D. Milman 1 ; Wiesław Pawłucki 2

1 Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
2 Institute of Mathematics, Jagiellonian University, 30-348 Kraków, Poland 
@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},
     publisher = {mathdoc},
     volume = {164},
     number = {1},
     year = {2006},
     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
PB  - mathdoc
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
%I mathdoc
%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. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.361/

Cité par Sources :