Intrinsic Characterization of Manifold-Valued Generalized Functions

• Autores: Michael Kunzinger, Roland Steinbauer, James A. Vickers
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 87, Nº 2, 2003, págs. 451-470
• Idioma: inglés
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• Resumen

  • 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 (analogous to 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.