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Azagra Rueda, Daniel and Fabián, M. and Jiménez Sevilla, María del Mar (2005) Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces. Canadian Mathematical Bulletin, 48 (4). pp. 481499. ISSN 00084395

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Abstract
We establish sufficient conditions on the shape of a set A included in
the space Ln s (X; Y ) of the nlinear symmetric mappings between Banach spaces
X and Y , to ensure the existence of a Cnsmooth mapping f : X ¡! Y , with bounded support, and such that f(n)(X) = A, provided that X admits a Cn smooth bump with bounded nth derivative and densX = densLn(X; Y ). For instance, when X is infinitedimensional, every bounded connected and open set U containing the origin is the range of the nth derivative of such a mapping.
The same holds true for the closure of U, provided that every point in the boundary of U is the end point of a path within U. In the finitedimensional case, more restrictive conditions are required. We also study the Fr´echet smooth case for mappings from Rn to a separable infinitedimensional Banach space and the Gˆateaux smooth case for mappings defined on a separable infinitedimensional
Banach space and with values in a separable Banach space.
Item Type:  Article 

Uncontrolled Keywords:  Starlike Bodies; Range; Theorem; Bump 
Subjects:  Sciences > Mathematics > Functional analysis and Operator theory 
ID Code:  12927 
Deposited On:  11 Jul 2011 08:06 
Last Modified:  06 Feb 2014 09:36 
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