Mathematics – Functional Analysis
Scientific paper
2001-04-27
Proceedings of the International Conference on Generalized Functions (ICGF 2000), edited by A. Delcroix, M. Hasler, J.-A. Mart
Mathematics
Functional Analysis
9 pages. Contribution to Proceedings of ICGF 2000
Scientific paper
We 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 $\xi$ on $X$ there exists a derivation operator $\hat L_\xi: \hat {\mathcal G} \to \hat {\mathcal G}$ which is linear and satisfies the Leibniz rule. (iii) $L_\xi$ 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 $X$.
No associations
LandOfFree
Diffeomorphism invariant Colombeau algebras. Part III: Global theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Diffeomorphism invariant Colombeau algebras. Part III: Global theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffeomorphism invariant Colombeau algebras. Part III: Global theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-437004