Extensions de jets dans des intersections de classes non quasi-analytiques (Q2724132)

\textit{J. Chaumat} and \textit{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 \textit{W. Pawłucki} and \textit{W. Pleśniak} [Stud. Math. 88, No. 3, 279-287 (1988; Zbl 0778.26010)] and \textit{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 \textit{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 \(\mathbb{R}^n\setminus E\).