Intrinsic characterization of manifold-valued generalized functions
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.
Cite
@article{arxiv.math/0205223,
title = {Intrinsic characterization of manifold-valued generalized functions},
author = {Michael Kunzinger and Roland Steinbauer and James A. Vickers},
journal= {arXiv preprint arXiv:math/0205223},
year = {2007}
}
Comments
LaTeX, 23 pages