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Approximation of functions and their derivatives by analytic maps on certain Banach spaces

Azagra Rueda, Daniel and Fry, Robb and Keener , L. (2011) Approximation of functions and their derivatives by analytic maps on certain Banach spaces. Bulletin of the London Mathematical Society, 43 (5). pp. 953-964. ISSN 0024-6093

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Abstract

Let X be a separable Banach space that admits a separating polynomial; in particular, let X be a separable Hilbert space. Let f : X -> R be bounded and Lipschitz, with uniformly continuous derivative. Then, for each epsilon > 0, there exists an analytic function g : X -> R with vertical bar g - f vertical bar < epsilon and parallel to g' - f'parallel to < epsilon.

Item Type:Article
Uncontrolled Keywords:Differentiable functions; Polynomials; Extensions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:13950
Deposited On:23 Nov 2011 12:28
Last Modified:06 Feb 2014 09:56

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