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
Official URL: http://blms.oxfordjournals.org/
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.
|Uncontrolled Keywords:||Differentiable functions; Polynomials; Extensions|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
|Deposited On:||23 Nov 2011 13:28|
|Last Modified:||23 Nov 2011 13:28|
Repository Staff Only: item control page