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Intersections de classes non quasi-analytiques

Abstract : In the case of intersections of non quasi-analytic classes of ultradifferentiable functions with moderate growth, J. Chaumat and A. M. Chollet prove, among other things, a Whitney extension theorem, for jets on a compact set 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 Whitney jet belongs to one of them. Then, by adopting a method of Lagrange interpolation polynomials due to W. Pawlucki et W. Plesniak, 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 the complementary of the compact. Those results are completed by three examples of non-existence of a linear continuous extension. Then we prove a Lojasiewicz theorem. All the results are closely related to already know facts of the theory of infinitely differentiable functions
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Contributor : Pascal BEAUGENDRE Connect in order to contact the contributor
Submitted on : Monday, April 29, 2002 - 8:10:10 PM
Last modification on : Saturday, April 20, 2019 - 1:23:39 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:20:34 PM


  • HAL Id : tel-00001335, version 1



Pascal Beaugendre. Intersections de classes non quasi-analytiques. Mathématiques [math]. Université Paris Sud - Paris XI, 2002. Français. ⟨tel-00001335⟩



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