[Banach] Abstract of a paper by D. Azagra, R. Fry and L. Keener

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