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

• Autorzy: P. Beaugendre
• Języki publikacji: FR EN

Abstrakty

EN

In [3], J. Chaumat and A.-M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact subset E of ℝⁿ, in the case of intersections of non-quasi-analytic classes with moderate growth and a Łojasiewicz 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 $C^{∞}$-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 ℝⁿ∖E. Then we prove a Łojasiewicz theorem.

Kategorie tematyczne

• 46E15: Banach spaces of continuous, differentiable or analytic functions
• 41A10: Approximation by polynomials
• 46E10: Topological linear spaces of continuous, differentiable or analytic functions
• 26E10: C ∞ -functions, quasi-analytic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2001
• Tom: 76
• Numer: 3
• Strony: 213-243

Daty

wydano

2001

Twórcy

autor

P. Beaugendre

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

Identyfikatory

DOI

10.4064/ap76-3-4