Isomorphisms of algebras of Colombeau generalized functions

Abstract

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.

10 pages

References in corpus (1)

• The use of Generalised Functions and Distributions in General Relativity

Cited by in corpus (4)

• Internal sets and internal functions in Colombeau theory
• Algebras of generalized functions with smooth parameter dependence
• An algebraic approach to manifold-valued generalized functions
• Point value characterizations and related results in the full Colombeau algebras G^e and G^d