Restrictions of smooth functions to a closed subset
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 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: 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
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     title = {Restrictions of smooth functions to a closed subset},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2067/

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