Colombeau algebras on a \(C^{\infty{}}\)-manifold
type: Item
instance of: scholarly article
title: Colombeau algebras on a \(C^{\infty{}}\)-manifold
zbMATH Open document ID: 0761.46022
DOI: 10.1016/0019-3577(91)90022-Y
author: J. W. de Roever
author: M. Damsma
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: The notion of a distribution in the sense of Colombeau is extended to an arbitrary \(C^ \infty\)-manifold \(X\). The set \({\mathcal G}\) of all such distributions is defined as a quotient sheaf \({\mathcal M}/{\mathcal N}\) of algebras \({\mathcal M}\) and \({\mathcal N}\). The existence of an injective sheaf morphism \(\sigma:{\mathcal D}'\to{\mathcal G}\) on \(X\) is proved such that for any section \(u\in{\mathcal D}'(\Omega)\), \(\Omega\subset X\), \(\sigma(u)\sim u\) holds, and that \(\sigma\) is the identity on the subsheaves \(C^ \infty\) of \(C^ \infty\)-functions in \({\mathcal D}'\) and \({\mathcal G}\). A theorem for submanifolds \(Y\subset X\) is also provided.
reviewed by: Julian Musielak
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 57316
zbMATH Keywords: Colombeau algebras
zbMATH Keywords: distribution in the sense of Colombeau
zbMATH Keywords: \(C^ \infty\)-manifold
zbMATH Keywords: quotient sheaf
zbMATH Keywords: injective sheaf morphism
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 57316