In this paper we obtain results on approximation, in the multidimensional complex case, of functions from 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 . In addition to the property (HCP), a crucial role will be played by a new geometrical criterion over the compact (property (ŁS)).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-4,
author = {Moulay Ta\"\i b Belghiti and Boutayeb El Ammari and Laurent P. Gendre},
title = {Approximation polyn\^omiale dans des classes de jets},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {43-62},
zbl = {1336.32013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-4}
}
Moulay Taïb Belghiti; Boutayeb El Ammari; Laurent P. Gendre. Approximation polynômiale dans des classes de jets. Banach Center Publications, Tome 104 (2015) pp. 43-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-4/