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Proceedings of the London Mathematical Society 2003 87(2):451-470; doi:10.1112/S0024611503014229
© 2003 by London Mathematical Society
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© London Mathematical Society

Intrinsic Characterization of Manifold-Valued Generalized Functions

Michael Kunzinger, Roland Steinbauer and James A. Vickers

Department of Mathematics, University of Vienna Strudhofg. 4, A-1090 Wien, Austria. E-mail: michael.kunzinger{at}univie.ac.at
Department of Mathematics, University of Vienna Strudhofg. 4, A-1090 Wien, Austria. E-mail: roland.steinbauer{at}univie.ac.at
Faculty of Mathematical Studies, University of Southampton Highfield, Southampton SO17 1BJ. E-mail: J.A.Vickers{at}maths.soton.ac.uk

Received 29 April 2002. Revision received 11 November 2002.

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. 2000 Mathematics Subject Classification 46T30 (primary), 46F30, 53B20 (secondary).

Key Words: algebras of generalized functions • Colombeau algebras • generalized functions on manifolds


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