Approximation polynômiale dans des classes de jets
Volume 107 / 2015
Abstract
In this paper we obtain results on approximation, in the multidimensional complex case, of functions from $\mathcal{A}^{\infty}(K)$ by complex polynomials. In particular, we generalize the results of Pawłucki and Pleśniak (1986) for the real case and of Siciak (1993) in the case of one complex variable. Furthermore, we extend the results of Baouendi and Goulaouic (1971) who obtained the order of approximation in the case of Gevrey classes over real compacts with smooth analytic boundary and we present the orders of approximation of certain intermediate classes of holomorphic ultradifferentiable jets $\mathcal{H}_{M}(K)$. In addition to the property (HCP), a crucial role will be played by a new geometrical criterion over the compact (property (ŁS)).
