Approximation of functions and their derivatives by analytic maps on certain Banach spaces

2010/11/20 by Azagra, D., Fry, R., Keener, L.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1011.4613

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 ε>0, there exists an analytic function g:X → R with |g-f|

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