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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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Official URL: http://blms.oxfordjournals.org/

## 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 |
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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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