Approximation polynômiale dans des classes de jets

• Autorzy: Moulay Taïb Belghiti , Boutayeb El Ammari , Laurent P. Gendre
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain results on approximation, in the multidimensional complex case, of functions from $𝓐^{∞}(K)$ 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 $𝓗_{M}(K)$. In addition to the property (HCP), a crucial role will be played by a new geometrical criterion over the compact (property (ŁS)).

Kategorie tematyczne

• 32U15: General pluripotential theory
• 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation
• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 43-62

Daty

wydano

2015

Twórcy

autor

Moulay Taïb Belghiti

• EECOMAS Lab, ENSA, Université Ibn Tofail, 14000 Kénitra, Maroc

autor

Boutayeb El Ammari

• EECOMAS Lab, ENSA, Université Ibn Tofail, 14000 Kénitra, Maroc

autor

Laurent P. Gendre

• Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse CEDEX 09, France

Identyfikatory

DOI

10.4064/bc107-0-4