Kergin interpolation in Banach spaces

Volume 153 / 2002

Henrik Petersson Studia Mathematica 153 (2002), 101-114 MSC: 46G20, 46E50, 46M35. DOI: 10.4064/sm153-2-1


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.


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

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