Kergin interpolation in Banach spaces

• Autorzy: Henrik Petersson
• Języki publikacji: EN

Abstrakty

EN

We study the Kergin operator on the space $H_{Nb}(E)$ 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.

Kategorie tematyczne

• 46G20: Infinite-dimensional holomorphy
• 46E50: Spaces of differentiable or holomorphic functions on infinite-dimensional spaces
• 46M35: Abstract interpolation of topological vector spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 153
• Numer: 2
• Strony: 101-114

Daty

wydano

2002

Twórcy

autor

Henrik Petersson

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

Identyfikatory

DOI

10.4064/sm153-2-1