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

Azagra D. | Zendy; Fry R. | Zendy; Keener L. | Zendy

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

Author(s) -

Azagra D.,

Fry R.,

Keener L.

Publication year - 2011

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdr032

Subject(s) - mathematics , banach space , separable space , lipschitz continuity , bounded function , hilbert space , polynomial , pure mathematics , analytic function , space (punctuation) , discrete mathematics , mathematical analysis , philosophy , linguistics

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 ε > 0, there exists an analytic function g : X → ℝ with | g − f | < ε and ‖ g ′ − f ′ ‖ < ε.

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