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Extensions de jets dans des intersections de classes non quasi-analytiques. (English) Zbl 0995.26017
J. Chaumat and A.-M. Chollet [Bull. Sci. Math. 122, No. 6, 455-485 (1998; Zbl 0930.26013)] proved versions of the Whitney Extension Theorem and the Łojasiewicz Pieceing Together Theorem for \(C^\infty\) jets on compact subsets of \(\mathbb{R}^n\) belonging to the intersections of non quasi-analytic classes with moderate growth. In this paper, the author considers the intersections of more general classes of Whitney jets and proves the above mentioned results in such a setting. Then, by adopting a method of Lagrange interpolation polynomials with Fekete nodes due to W. Pawłucki and W. Pleśniak [Stud. Math. 88, No. 3, 279-287 (1988; Zbl 0778.26010)] and W. Pleśniak [Bull. Soc. R. Sci. Liège 63, No. 5, 393-402 (1994; Zbl 0816.26009)], he also constructs a continuous linear extension operator for jets defined on a Markov compact subset \(E\) of \(\mathbb{R}^n\) belonging to the considered intersections. As in the case of ultradifferentiable jets considered by M. Valdivia [Math. Jap. 44, No. 3, 415-434 (1996; Zbl 0874.46027)], the above extension can also be chosen to be (real) analytic on \(\mathbb{R}^n\setminus E\).

MSC:
26E10 \(C^\infty\)-functions, quasi-analytic functions
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46F05 Topological linear spaces of test functions, distributions and ultradistributions
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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