11 research outputs found
An algebraic approach to manifold-valued generalized functions
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.Comment: 7 page
Isomorphisms of algebras of Colombeau generalized functions
We show that for smooth manifolds X and Y, any isomorphism between the
special algebra of Colombeau generalized functions on X, resp. Y is given by
composition with a unique Colombeau generalized function from Y to X. We also
identify the multiplicative linear functionals from the special algebra of
Colombeau generalized functions on X to the ring of Colombeau generalized
numbers. Up to multiplication with an idempotent generalized number, they are
given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page