20.500.12556/DiRROS-18418 Reflexivity of the space of transversal distributions For any smooth, Hausdorff and second-countable manifold $N$ one can define the Fréchet space ${\mathcal C}^{\infty}(N)$ of smooth functions on $N$ and its strong dual ${\cal E}'(N)$ of compactly supported distributions on $N$. It is a standard result that the strong dual of ${\cal E}'(N)$ is naturally isomorphic to ${\mathcal C}^{\infty}(N)$, which implies that both ${\mathcal C}^{\infty}(N)$ and ${\cal E}'(N)$ are reflexive locally convex spaces. In this paper we generalise that result to the setting of transversal distributions on the total space of a surjective submersion $\pi : P\to M$. We show that the strong ${\mathcal C}^{\infty}_c(M)$-dual of the space ${\cal E}'_{\pi} (P)$ of $\pi$-transversal distributions is naturally isomorphic to the ${\mathcal C}^{\infty}_c(M)$-module ${\mathcal C}^{\infty}(P)$. distributions with compact support Fréchet spaces transversal distributions homomorphisms of modules reflexive modules true false true Angleški jezik Ni določen Neznano 2024-03-15 12:34:32 2024-03-15 12:34:32 2024-03-16 03:37:16 0000-00-00 00:00:00 2023 0 0 20 str. iss. 10, article no. 331 Vol. 33 Oct. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-10-01 517.9 1050-6926 10.1007/s12220-023-01390-y 178959107 https://link.springer.com/article/10.1007/s12220-023-01390-y 1 ff6945f6-e2bf-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25084 s12220-023-01390-y-1.pdf s12220-023-01390-y-1.pdf 1 CE0285495983EE8EC68AB2CF5A861455 d54da663151fe1874b928adc351a8b9d0c3e12d253a43673e9c3d6f9eb210b70 41522657-e2c0-11ee-9dd4-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25086 Inštitut za matematiko, fiziko in mehaniko 0 0 0