| Título: | Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces |
| Autores: | Azagra Rueda, Daniel ; Fabián, M. ; Jiménez Sevilla, María del Mar |
| Tipo de documento: | texto impreso |
| Editorial: | University of Toronto Press, 2005 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores , Tipo = Artículo |
| Resumen: |
We establish sufficient conditions on the shape of a set A included in the space Ln s (X; Y ) of the n-linear symmetric mappings between Banach spaces X 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-dimensional Banach space and with values in a separable Banach space. |
| En línea: | https://eprints.ucm.es/id/eprint/12927/1/2005exactfilling.pdf |
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