Isomorphisms of algebras of Colombeau generalized functions
Functional Analysis
2017-05-24 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.math/0612646,
title = {Isomorphisms of algebras of Colombeau generalized functions},
author = {Hans Vernaeve},
journal= {arXiv preprint arXiv:math/0612646},
year = {2017}
}
Comments
10 pages