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

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

2010-11-20

arxiv.org/abs/1011.4613v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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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