Restrictions of smooth functions to a closed subset

Izumi, Shuzo

doi:10.5802/aif.2067

Restrictions of smooth functions to a closed subset
[Restrictions de fonctions différentiables à un sous ensemble fermé]

Izumi, Shuzo ¹

¹ Kinki University,Department of Mathematics, Kowakae Higashi-Osaka 577-8502 (Japan)

Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 1811-1826.

Résumé
Abstract

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.

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.

MR Zbl

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
Mot clés : Problème de Whitney, théorème de Spallek, fonction différentiable, fibré paratangent d'ordre supérieur, platitude, matrice de Vandermonde multi-dimensionnelle

Affiliations des auteurs :

Izumi, Shuzo ¹

¹ Kinki University,Department of Mathematics, Kowakae Higashi-Osaka 577-8502 (Japan)

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     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 = {https://www.numdam.org/articles/10.5802/aif.2067/}
}

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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. https://www.numdam.org/articles/10.5802/aif.2067/

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