Reflexivity of the space of transversal distributions

Kališnik, Jure (avtor)

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 ${\mathcal C}^{\infty}(P)$.

• Jezik: Angleški jezik
• Ključne besede: distributions with compact support, Fréchet spaces, transversal distributions, homomorphisms of modules, reflexive modules
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2023
• Št. strani: 20 str.
• Številčenje: Vol. 33, iss. 10, art. 331
• PID: 20.500.12556/RUL-153557
• UDK: 517.9
• ISSN pri članku: 1050-6926
• DOI: 10.1007/s12220-023-01390-y
• COBISS.SI-ID: 178959107
• Datum objave v RUL: 15.01.2024

Gradivo je del revije

• Naslov: The journal of geometric analysis
• Skrajšan naslov: J. geom. anal.
• Založnik: Springer Nature, Mathematica Josephina
• ISSN: 1050-6926
• COBISS.SI-ID: 30685696

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.