A global theory of algebras of generalized functions

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dc.creatorGrosser, Michael
dc.creatorKunzinger, Michael
dc.creatorSteinbauer, Roland
dc.creatorVickers, James
dc.date1999-12-28
dc.date.accessioned2026-07-07T05:32:31Z
dc.date.available2026-07-07T05:32:31Z
dc.descriptionWe present a geometric approach to defining an algebra $\hat{\mathcal G}(M)$ (the Colombeau algebra) of generalized functions on a smooth manifold $M$ containing the space ${\mathcal D}'(M)$ of distributions on $M$. Based on differential calculus in convenient vector spaces we achieve an intrinsic construction of $\hat{\mathcal G}(M)$. $\hat{\mathcal G}(M)$ is a{\em differential} algebra, its elements possessing Lie derivatives with respect to arbitrary smooth vector fields. Moreover, we construct a canonical linear embedding of ${\mathcal D}'(M)$ into $\hat{\mathcal G}(M)$ that renders ${\mathcal C}^\infty (M)$ a faithful subalgebra of $\hat{\mathcal G}(M)$. Finally, it is shown that this embedding commutes with Lie derivatives. Thus $\hat{\mathcal G}(M)$ retains all the distinguishing properties of the local theory in a global context.
dc.description24 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/9912216
dc.identifierhttp://arxiv.org/abs/math/9912216
dc.identifierAdvances in Math. 166 (2002) 50-72
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79683
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subject46F30; 46T30
dc.titleA global theory of algebras of generalized functions
dc.typetext

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