This is an announcement for the paper "Approximation of functions and their derivatives by analytic maps on certain Banach spaces" by D. Azagra, R. Fry and L. Keener.

Abstract: Let X be a separable Banach space which admits a separating polynomial; in particular X a separable Hilbert space. Let f:X→R be bounded, Lipschitz, and C¹ with uniformly continuous derivative. Then for each {\epsilon}>0, there exists an analytic function g:X→R with |g-f|<{\epsilon} and ‖g′-f′‖<{\epsilon}.

Archive classification: math.FA

Remarks: 17 pages

Submitted from: rfry@tru.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1011.4613

or

http://arXiv.org/abs/1011.4613