Kergin interpolation in Banach spaces

Henrik Petersson. "Kergin interpolation in Banach spaces." Studia Mathematica 153.2 (2002): 101-114. <http://eudml.org/doc/285281>.

@article{HenrikPetersson2002,
abstract = {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.},
author = {Henrik Petersson},
journal = {Studia Mathematica},
keywords = {interpolation; Kergin operator; holomorphic; nuclearly entire functions; exponential type; Fourier-Borel transform; convolution operator; PDE-preserving},
language = {eng},
number = {2},
pages = {101-114},
title = {Kergin interpolation in Banach spaces},
url = {http://eudml.org/doc/285281},
volume = {153},
year = {2002},
}

TY - JOUR
AU - Henrik Petersson
TI - Kergin interpolation in Banach spaces
JO - Studia Mathematica
PY - 2002
VL - 153
IS - 2
SP - 101
EP - 114
AB - 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.
LA - eng
KW - interpolation; Kergin operator; holomorphic; nuclearly entire functions; exponential type; Fourier-Borel transform; convolution operator; PDE-preserving
UR - http://eudml.org/doc/285281
ER -