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 13:28 |
| Last Modified: | 23 Nov 2011 13:28 |
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