Kergin interpolation in Banach spaces

Henrik Petersson¹

¹ School of Mathematics and Systems Engineering SE-351 95 Växjö, Sweden

Studia Mathematica, Tome 153 (2002) no. 2, pp. 101-114

Résumé

We study the Kergin operator on the space $H_{\rm Nb}(E)$ of nuclearly entire functions of bounded type on a Banach space $E$. We show that the Kergin operator is a projector with interpolating properties and that it preserves homogeneous solutions to homogeneous differential operators. Further, we show that the Kergin operator is uniquely determined by these properties. We give error estimates for approximating a function by its Kergin polynomial and show in this way that for any given bounded sequence of interpolation points and any nuclearly entire function, the corresponding sequence of Kergin polynomials converges.

Détail

DOI : 10.4064/sm153-2-1

Mots-clés : study kergin operator space nuclearly entire functions bounded type banach space kergin operator projector interpolating properties preserves homogeneous solutions homogeneous differential operators further kergin operator uniquely determined these properties error estimates approximating function its kergin polynomial given bounded sequence interpolation points nuclearly entire function corresponding sequence kergin polynomials converges