An algebraic approach to manifold-valued generalized functions
arXiv:1010.3562 · doi:10.1007/s00605-011-0317-1
Abstract
We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.
7 pages