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Intrinsic characterization of manifold-valued generalized functions

Intrinsic characterization of manifold-valued generalized functions
Intrinsic characterization of manifold-valued generalized functions
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.
algebras of generalized functions, colombeau algebras, generalized functions on manifolds
0024-6115
451-470
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634

Kunzinger, Michael, Steinbauer, Roland and Vickers, James A. (2003) Intrinsic characterization of manifold-valued generalized functions. Proceedings of the London Mathematical Society, 87 (2), 451-470. (doi:10.1112/S0024611503014229).

Record type: Article

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 (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.

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More information

Published date: September 2003
Keywords: algebras of generalized functions, colombeau algebras, generalized functions on manifolds

Identifiers

Local EPrints ID: 29337
URI: http://eprints.soton.ac.uk/id/eprint/29337
ISSN: 0024-6115
PURE UUID: a76b88cd-73ea-4126-b456-af5fe0c6bbd2
ORCID for James A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 12 May 2006
Last modified: 18 Feb 2021 16:33

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