Intrinsic characterization of manifold-valued generalized functions

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The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of manifold-valued generalized functions and of generalized vector bundle homomorphisms. As a consequence, a characterization of equivalence that does not resort to derivatives (already known for the scalar-valued cases of Colombeau's construction) is achieved. These results are employed to derive a point value description of all types of generalized functions valued in manifolds and to show that composition can be carried out unrestrictedly. Finally, a new concept of association adapted to the present setting is introduced.
LaTeX, 23 pages

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Functional Analysis, Mathematical Physics, 46T30; 46F30; 53B20

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http://salesiana.dossiersoluciones.com/handle/123456789/64118

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205223
 http://arxiv.org/abs/math/0205223
 Proc. London Math. Soc. 87 (2), 451-470, 2003

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arXiv