Extensions de jets dans des intersections de classes non quasi-analytiques

P. Beaugendre¹

¹ Mathématiques Université de Paris-Sud Bâtiment 425 91405 Orsay, France

Annales Polonici Mathematici, Tome 76 (2001) no. 3, pp. 213-243

Résumé

In $[3] $, J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset $E$ of ${\mathbb R}^{n}$, in the case of intersections of non-quasi-analytic classes with moderate growth and a /Lojasiewicz theorem in the regular situation. These intersections are included in the intersection of Gevrey classes. Here we prove an extension theorem in the case of more general intersections such that every $C^{\infty }$-Whitney jet belongs to one of them. We also prove a linear extension theorem in the case of a compact set with Markov's property. These extensions of jets can be chosen to be real-analytic on ${\mathbb R}^{n}\setminus E$. Then we prove a /Lojasiewicz theorem.

Détail

DOI : 10.4064/ap76-3-4

Mots-clés : chaumat m chollet prove among other things whitney extension theorem jets compact subset mathbb intersections non quasi analytic classes moderate growth lojasiewicz theorem regular situation these intersections included intersection gevrey classes here prove extension theorem general intersections every infty whitney jet belongs prove linear extension theorem compact set markovs property these extensions jets chosen real analytic mathbb setminus prove lojasiewicz theorem