Lagrange approximation in Banach spaces

Abstract

Starting from Lagrange interpolation of the exponential function ez 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.