Kernel Theorems in Spaces of Tempered Generalized Functions
| dc.creator | Delcroix, Antoine | |
| dc.date | 2006-03-02 | |
| dc.date.accessioned | 2026-07-07T13:05:19Z | |
| dc.date.available | 2026-07-07T13:05:19Z | |
| dc.description | In analogy to the classical isomorphism between $\mathcal{L}(\mathcal{S}(\mathbb{R}^{n}) ,\mathcal{S}^{\prime}(\mathbb{R}^{m}) ) $ and $\mathcal{S}^{\prime}(\mathbb{R}^{n+m}) $, we show that a large class of moderate linear mappings acting between the space $\mathcal{G}\_{\mathcal{S}}(\mathbb{R}^{n}) $ of Colombeau rapidly decreasing generalized functions and the space $\mathcal{G}\_τ(\mathbb{R}^{n}) $ of temperate ones admits generalized integral representations, with kernels belonging to $\mathcal{G}\_τ(\mathbb{R}^{n+m}) $. Furthermore, this result contains the classical one in the sense of the generalized distribution equality. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0603035 | |
| dc.identifier | http://arxiv.org/abs/math/0603035 | |
| dc.identifier | Math. Proc. Camb. Philos. Soc. 142, 3 (2007) 557-572 | |
| dc.identifier | doi:10.1017/S0305004107000011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227453 | |
| dc.subject | Functional Analysis | |
| dc.subject | 45P05; 46F05; 46F30; 47G10 | |
| dc.title | Kernel Theorems in Spaces of Tempered Generalized Functions | |
| dc.type | text |