RT Journal Article
T1 Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
A1 Azagra Rueda, Daniel
A1 Fabián, M.
A1 Jiménez Sevilla, María del Mar
AB We establish sufficient conditions on the shape of a set A included inthe space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spacesX and Y , to ensure the existence of a Cn-smooth mapping f : X ¡! Y , with bounded support, and such that f(n)(X) = A, provided that X admits a Cn- smooth bump with bounded n-th derivative and densX = densLn(X; Y ). For instance, when X is infinite-dimensional, every bounded connected and open set U containing the origin is the range of the n-th 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 finite-dimensional case, more restrictive conditions are required. We also study the Fr´echet smooth case for mappings from Rn to a separable infinite-dimensional Banach space and the Gˆateaux smooth case for mappings defined on a separable infinite-dimensionalBanach space and with values in a separable Banach space.
PB University of Toronto Press
SN 0008-4395
YR 2005
FD 2005
LK https://hdl.handle.net/20.500.14352/49708
UL https://hdl.handle.net/20.500.14352/49708
LA eng
NO GA CR 201/01/1198
DS Docta Complutense
RD 3 may 2024