Lagrange approximation in Banach spaces

Lisa Nilsson; Damián Pinasco; Ignacio M. Zalduendo

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 281-288
  • ISSN: 0011-4642

Abstract

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Starting from Lagrange interpolation of the exponential function e z in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space E . Given such a representable entire funtion f : E → ℂ , in order to study the approximation problem and the uniform convergence of these polynomials to f on bounded sets of E , we present a sufficient growth condition on the interpolating sequence.

How to cite

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Nilsson, Lisa, Pinasco, Damián, and Zalduendo, Ignacio M.. "Lagrange approximation in Banach spaces." Czechoslovak Mathematical Journal 65.1 (2015): 281-288. <http://eudml.org/doc/270047>.

@article{Nilsson2015,
abstract = {Starting from Lagrange interpolation of the exponential function $\{\rm e\}^z$ in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space $E$. Given such a representable entire funtion $f\colon E \rightarrow \mathbb \{C\}$, in order to study the approximation problem and the uniform convergence of these polynomials to $f$ on bounded sets of $E$, we present a sufficient growth condition on the interpolating sequence.},
author = {Nilsson, Lisa, Pinasco, Damián, Zalduendo, Ignacio M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Lagrange interpolation; Lagrange approximation; Kergin interpolation; Kergin approximation; Banach space},
language = {eng},
number = {1},
pages = {281-288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Lagrange approximation in Banach spaces},
url = {http://eudml.org/doc/270047},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Nilsson, Lisa
AU - Pinasco, Damián
AU - Zalduendo, Ignacio M.
TI - Lagrange approximation in Banach spaces
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 281
EP - 288
AB - Starting from Lagrange interpolation of the exponential function ${\rm e}^z$ in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space $E$. Given such a representable entire funtion $f\colon E \rightarrow \mathbb {C}$, in order to study the approximation problem and the uniform convergence of these polynomials to $f$ on bounded sets of $E$, we present a sufficient growth condition on the interpolating sequence.
LA - eng
KW - Lagrange interpolation; Lagrange approximation; Kergin interpolation; Kergin approximation; Banach space
UR - http://eudml.org/doc/270047
ER -

References

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