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arXiv · 1011.4613

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

D. Azagra·R. Fry·L. Keener
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Abstract

Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let $f:X \rightarrow R$ be bounded, Lipschitz, and $C^1$ with uniformly continuous derivative. Then for each {\epsilon}>0, there exists an analytic function $g:X \rightarrow R$ with $|g-f|<\epsilon$ and $||g'-f'||<\epsilon$.

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D. Azagra, R. Fry, L. Keener. 2010-11-20. Approximation of functions and their derivatives by analytic maps on certain Banach spaces. https://arxiv.org/abs/1011.4613

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