We study the Kergin operator on the space 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-1,
author = {Henrik Petersson},
title = {Kergin interpolation in Banach spaces},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {101-114},
zbl = {1085.46032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-1}
}
Henrik Petersson. Kergin interpolation in Banach spaces. Studia Mathematica, Tome 151 (2002) pp. 101-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm153-2-1/