Restrictions of smooth functions to a closed subset
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, p. 1811-1826
We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on C d 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.
Nous proposons une approche d’une conjecture de Bierstone-Milman-Pawłucki sur le problème de Whitney concernant le prolongement C d 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.
DOI : https://doi.org/10.5802/aif.2067
Classification:  26B05
Keywords: Whitney's problem, Spallek's theorem, smooth functions, higher order paratangent bundle, flatness, multi-dimensional Vandermonde matrix, self-similar set
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {6},
     year = {2004},
     pages = {1811-1826},
     doi = {10.5802/aif.2067},
     zbl = {1083.26009},
     mrnumber = {2134225},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_6_1811_0}
}
Izumi, Shuzo. Restrictions of smooth functions to a closed subset. Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 1811-1826. doi : 10.5802/aif.2067. http://www.numdam.org/item/AIF_2004__54_6_1811_0/

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