IM PAN
INSTITUTE OF MATHEMATICS, POLISH ACADEMY OF SCIENCES
ANNALES
POLONICI MATHEMATICI
ISSN: 0066-2216(p) 1730-6272(e)
 

Extensions de jets dans des intersections de classes non quasi-analytiques
P. Beaugendre1
Ann. Polon. Math. 76 (2001), 213-243
doi:10.4064/ap76-3-4

Abstract: 
In $[3] $, J. Chaumat and A.-M. Chollet prove, among other
things, a Whitney extension theorem, for jets on a compact
subset $E$ of ${\sym R}^{n}$, 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 ${\sym
R}^{n}\setminus E$. Then we prove a /Lojasiewicz
theorem.


MSC (2000): 26E10, 41A10, 46E10, 46E15.
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  1. Mathématiques
    Université de Paris-Sud
    Bâtiment 425
    91405 Orsay, France
    , et