2001/04/27 by Michael Kunzinger
Mathematics · Physics and Astronomy · #math.FA #math-ph #math.MP #msc:46F30 #msc:46T30
published as Proceedings 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 · 9 pages. Contribution to Proceedings of ICGF 2000
arxiv created 2001/04/27 · arxiv updated 2009/11/30
We present the construction of an associative, commutative algebra \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 \mathcal G, f(p)≡ 1 is the unity in the algebra. (ii) For every smooth vector field ξ on X there exists a derivation operator Lξ: \mathcal G → \mathcal G which is linear and satisfies the Leibniz rule. (iii) Lξ 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 \mathcal G are defined in purely intrinsic terms of the manifold X.