Geodesic
Manifold-valued generalized functions in full Colombeau spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 519-534.

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We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized vector bundle homomorphisms and, based on this, provide a definition of tangent map for such generalized functions.
Classification : 26E15, 46F30, 46T30
Keywords: algebras of generalized functions; manifold-valued generalized functions; full Colombeau algebras 
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Kunzinger, Michael; Nigsch, Eduard. Manifold-valued generalized functions in full Colombeau spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 4, pp. 519-534. http://geodesic.mathdoc.fr/item/CMUC_2011__52_4_a4/