Diffeomorphism invariant Colombeau algebras. Part III: Global theory

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dc.creatorKunzinger, Michael
dc.date2001-04-27
dc.date.accessioned2026-07-07T04:41:31Z
dc.date.available2026-07-07T04:41:31Z
dc.descriptionWe present the construction of an associative, commutative algebra $\hat {\mathcal G}$ of generalized functions on a manifold $X$ satisfying the following optimal set of permanence properties: (i)The space of distributions on $X$ is linearly embedded into $\hat {\mathcal G}$, $f(p)\equiv 1$ is the unity in the algebra. (ii) For every smooth vector field $ξ$ on $X$ there exists a derivation operator $\hat L_ξ: \hat {\mathcal G} \to \hat {\mathcal G}$ which is linear and satisfies the Leibniz rule. (iii) $L_ξ$ restricted to the space of distributions on $X$ is the usual Lie derivative. (iv) Multiplication in the algebra restricted to the space of smooth functions is the usual (pointwise) product of functions. Moreover, the basic building blocks of $\hat {\mathcal G}$ are defined in purely intrinsic terms of the manifold $X$.
dc.description9 pages. Contribution to Proceedings of ICGF 2000
dc.identifierhttps://arxiv.org/abs/math/0104272
dc.identifierhttp://arxiv.org/abs/math/0104272
dc.identifierProceedings of the International Conference on Generalized Functions (ICGF 2000), edited by A. Delcroix, M. Hasler, J.-A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 117-126, 2004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61387
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subject46F30; 46T30
dc.titleDiffeomorphism invariant Colombeau algebras. Part III: Global theory
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