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Monatshefte für Mathematik

, Volume 162, Issue 2, pp 225–237 | Cite as

Isomorphisms of algebras of generalized functions

  • Hans Vernaeve
Article

Abstract

We show that for smooth manifolds X and Y, any isomorphism between the algebras of generalized functions (in the sense of Colombeau) on X, resp. Y is given by composition with a unique generalized function from Y to X. We also characterize the multiplicative linear functionals from the Colombeau algebra on X to the ring of 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

Nonlinear generalized functions Algebra homomorphisms Multiplicative linear functionals Composition operators 

Mathematics Subject Classification (2000)

Primary 46F30 Secondary 46E25 54C40 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Ghent UniversityGentBelgium

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