Isomorphisms of algebras of Colombeau generalized functions

Details Isomorphisms of algebras of Colombeau generalized functions Isomorphisms of algebras of Colombeau generalized functions

2006-12-21

arxiv.org/abs/math/0612646v1

Mathematics

Functional Analysis

10 pages

Scientific paper

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.

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