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Intrinsic characterization of manifold-valued generalized functions

Michael Kunzinger·Roland Steinbauer·James A. Vickers
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Abstract

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.

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Michael Kunzinger, Roland Steinbauer, James A. Vickers. 2002-05-21. Intrinsic characterization of manifold-valued generalized functions. https://arxiv.org/abs/math/0205223

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