On the foundations of nonlinear generalized functions II
| dc.creator | Grosser, Michael | |
| dc.date | 1999-12-28 | |
| dc.date.accessioned | 2026-07-07T05:32:31Z | |
| dc.date.available | 2026-07-07T05:32:31Z | |
| dc.description | This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra $\mathcal{G}^d = \mathcal{E}_M/\mathcal{N}$ introduced in part I and Colombeau's original algebra $\mathcal{G}^e$. Three main results are established: First, a simple criterion describing membership in $\mathcal{N}$ (applicable to all types of Colombeau algebras) is given. Second, two counterexamples demonstrate that $\mathcal{G}^d$ is not injectively included in $\mathcal{G}^e$. Finally, it is shown that in the range ``between'' $\mathcal{G}^d$ and $\mathcal{G}^e$ only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of $\mathcal{G}^d$ on manifolds are derived. | |
| dc.description | 43 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/9912215 | |
| dc.identifier | http://arxiv.org/abs/math/9912215 | |
| dc.identifier | Mem. Amer. Math. Soc. 153, No. 729, 2001. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79682 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.subject | 46F30; 26E15; 46E50; 35D05 | |
| dc.title | On the foundations of nonlinear generalized functions II | |
| dc.type | text |