Geodesic
Lagrange approximation in Banach spaces
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 281-288
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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 $f\colon E \to \mathbb C$, 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.
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 $f\colon E \to \mathbb C$, 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.
DOI : 10.1007/s10587-015-0174-5
Classification : 30E10, 30E20, 46G20
Keywords: Lagrange interpolation; Lagrange approximation; Kergin interpolation; Kergin approximation; Banach space 
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Nilsson, Lisa; Pinasco, Damián; Zalduendo, Ignacio. Lagrange approximation in Banach spaces. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 281-288. doi: 10.1007/s10587-015-0174-5

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