Opérateurs linéaires continus d'extension dans des intersections de classes ultradifférentiables

Abstract

Mityagin proved that the Tchebyshev polynomials form a Schauder basis of the space of C ∞ functions on the interval [−1,1]. Thus, he deduced an explicit continuous linear extension operator. These results were extended, by Goncharov, to compact sets which do not satisfy the Markov's inequalities. On the other hand, Tidten gave examples of compact sets for which there is no continuous linear extension operator. In this Note, we generalize these works to ultradifferentiable classes of functions built on the model of the intersection of non quasi-analytic Gevrey classes. We get, among other things, a Whitney linear extension theorem for ultradifferentiable jets of Beurling type. To cite this article: P. Beaugendre, C. R. Acad. Sci. Paris, Ser. I 338 (2004).