Geodesic
An intrinsic definition of the Colombeau generalized functions
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 71-95.

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A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a \text{$\Cal C^\infty $} manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.
Classification : 46F05, 46F30, 46G05
Keywords: Colombeau generalized function; distribution; canonical embedding; manifold 
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Jelínek, Jiří. An intrinsic definition of the Colombeau generalized functions. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 71-95. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a5/