An algebraic approach to manifold-valued generalized functions

作者：Burtscher Annegret^*

来源：Monatshefte fur Mathematik, 2012, 166(3-4): 361-370.

DOI：10.1007/s00605-011-0317-1

• Nonlinear generalized functions
• Special Colombeau algebras
• Algebra homomorphisms
• Smooth functions
• Diffeomorphisms

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.

• 出版日期2012-6