20.500.12556/RUL-153557 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 Članek v reviji 2024-01-15 14:29:56 2024-01-15 14:29:58 2024-01-16 03:41:24 0000-00-00 00:00:00 2023 0 0 20 str. iss. 10, art. 331 Vol. 33 Oct. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9 1050-6926 10.1007/s12220-023-01390-y 178959107 s12220-023-01390-y.pdf s12220-023-01390-y.pdf 1 FBC339E8055A6D634328DBB58BEB42F8 3702ba38ac50a3c6512b41044431f2fb8151e33c6870942d173d8f68328f63ee 7670a808-b3aa-11ee-88ef-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=179614 https://link.springer.com/article/10.1007/s12220-023-01390-y 1 2ecd209c-b3aa-11ee-88ef-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=179613 Fakulteta za matematiko in fiziko 0 0 0