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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.

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Cite

@article{arxiv.math/0612646,
  title  = {Isomorphisms of algebras of Colombeau generalized functions},
  author = {Hans Vernaeve},
  journal= {arXiv preprint arXiv:math/0612646},
  year   = {2017}
}

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10 pages