Approximation polynômiale dans des classes de jets

Moulay Taïb Belghiti, Boutayeb El Ammari, and Laurent P. Gendre. "Approximation polynômiale dans des classes de jets." Banach Center Publications 107.1 (2015): 43-62. <http://eudml.org/doc/282263>.

@article{MoulayTaïbBelghiti2015,
abstract = {In this paper we obtain results on approximation, in the multidimensional complex case, of functions from $^\{∞\}(K)$ 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 $_\{M\}(K)$. In addition to the property (HCP), a crucial role will be played by a new geometrical criterion over the compact (property (ŁS)).},
author = {Moulay Taïb Belghiti, Boutayeb El Ammari, Laurent P. Gendre},
journal = {Banach Center Publications},
keywords = {approximation by complex polynomials; holomorphic ultradifferentiable jets},
language = {eng},
number = {1},
pages = {43-62},
title = {Approximation polynômiale dans des classes de jets},
url = {http://eudml.org/doc/282263},
volume = {107},
year = {2015},
}

TY - JOUR
AU - Moulay Taïb Belghiti
AU - Boutayeb El Ammari
AU - Laurent P. Gendre
TI - Approximation polynômiale dans des classes de jets
JO - Banach Center Publications
PY - 2015
VL - 107
IS - 1
SP - 43
EP - 62
AB - In this paper we obtain results on approximation, in the multidimensional complex case, of functions from $^{∞}(K)$ 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 $_{M}(K)$. In addition to the property (HCP), a crucial role will be played by a new geometrical criterion over the compact (property (ŁS)).
LA - eng
KW - approximation by complex polynomials; holomorphic ultradifferentiable jets
UR - http://eudml.org/doc/282263
ER -