Nous proposons une approche d’une conjecture de Bierstone-Milman-Pawłucki sur le problème de Whitney concernant le prolongement des fonctions. Elle permet de montrer que la conjecture est vraie pour des ensembles fractals classiques. Nous obtenons ensuite un raffinement d’un théorème de Spallek sur la platitude.
We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on extendability of functions. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek’s theorem on flatness.
Keywords: Whitney's problem, Spallek's theorem, smooth functions, higher order paratangent bundle, flatness, multi-dimensional Vandermonde matrix, self-similar set
Mot clés : Problème de Whitney, théorème de Spallek, fonction différentiable, fibré paratangent d'ordre supérieur, platitude, matrice de Vandermonde multi-dimensionnelle
@article{AIF_2004__54_6_1811_0, author = {Izumi, Shuzo}, title = {Restrictions of smooth functions to a closed subset}, journal = {Annales de l'Institut Fourier}, pages = {1811--1826}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {6}, year = {2004}, doi = {10.5802/aif.2067}, mrnumber = {2134225}, zbl = {1083.26009}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2067/} }
TY - JOUR AU - Izumi, Shuzo TI - Restrictions of smooth functions to a closed subset JO - Annales de l'Institut Fourier PY - 2004 SP - 1811 EP - 1826 VL - 54 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2067/ DO - 10.5802/aif.2067 LA - en ID - AIF_2004__54_6_1811_0 ER -
%0 Journal Article %A Izumi, Shuzo %T Restrictions of smooth functions to a closed subset %J Annales de l'Institut Fourier %D 2004 %P 1811-1826 %V 54 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2067/ %R 10.5802/aif.2067 %G en %F AIF_2004__54_6_1811_0
Izumi, Shuzo. Restrictions of smooth functions to a closed subset. Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1811-1826. doi : 10.5802/aif.2067. http://www.numdam.org/articles/10.5802/aif.2067/
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