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Isomorphisms of algebras of generalized functions

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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.

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Authors and Affiliations

  1. Ghent University, Krijgslaan 281, 9000, Gent, Belgium

    Hans Vernaeve

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  1. Hans Vernaeve
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Correspondence to Hans Vernaeve.

Additional information

Supported by research grants M949 and Y237 of the Austrian Science Fund (FWF).

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Vernaeve, H. Isomorphisms of algebras of generalized functions. Monatsh Math 162, 225–237 (2011). https://doi.org/10.1007/s00605-009-0152-9

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  • DOI: https://doi.org/10.1007/s00605-009-0152-9

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