2009
DOI: 10.1007/s00605-009-0152-9
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Isomorphisms of algebras of generalized functions

Abstract: 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… Show more

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Cited by 11 publications
(26 citation statements)
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“…Structure preserving maps between paracompact manifolds in Colombeau theory are the so-called compactly bounded (c-bounded) generalized functions [11,14,15]. Recently H. Vernaeve [20] established a correspondence analogous to the above theorems between manifold-valued generalized functions and the algebra homomorphisms of Colombeau algebras.…”
Section: Theorem 22 Let X and Y Be Any Hausdorff Smooth Manifolds (Nmentioning
confidence: 93%
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“…Structure preserving maps between paracompact manifolds in Colombeau theory are the so-called compactly bounded (c-bounded) generalized functions [11,14,15]. Recently H. Vernaeve [20] established a correspondence analogous to the above theorems between manifold-valued generalized functions and the algebra homomorphisms of Colombeau algebras.…”
Section: Theorem 22 Let X and Y Be Any Hausdorff Smooth Manifolds (Nmentioning
confidence: 93%
“…On the other hand, as mentioned above, H. Vernaeve [20] provided Theorem 2.3 characterizing morphisms between special Colombeau algebras (with non-smooth parametrization) with locally defined c-bounded generalized functions. As in the classical case, the idea was to identify 'points' in a manifold X with 'algebraic objects' in the algebra G(X )-and similarly for Y -in order to construct a 'structure preserving map' between Y and X given an algebra homomorphism between G(X ) and G(Y ).…”
Section: Isomorphisms Of Algebras Of Colombeau Generalized Functionsmentioning
confidence: 95%
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