| Naslov: | Reflexivity of the space of transversal distributions |
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| Avtorji: | ID Kališnik, Jure (Avtor) |
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| Datoteke: |  URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s12220-023-01390-y
 PDF - Predstavitvena datoteka, prenos (332,43 KB)
MD5: CE0285495983EE8EC68AB2CF5A861455
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | 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 ${\mathcal C}^{\infty}(P)$. |
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| Ključne besede: | distributions with compact support, Fréchet spaces, transversal distributions, homomorphisms of modules, reflexive modules |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.10.2023 |
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| Leto izida: | 2023 |
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| Št. strani: | 20 str. |
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| Številčenje: | Vol. 33, iss. 10, article no. 331 |
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| PID: | 20.500.12556/DiRROS-18418  |
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| UDK: | 517.9 |
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| ISSN pri članku: | 1050-6926 |
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| DOI: | 10.1007/s12220-023-01390-y |
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| COBISS.SI-ID: | 178959107 |
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| Opomba: |
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| Datum objave v DiRROS: | 15.03.2024 |
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| Število ogledov: | 1083 |
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| Število prenosov: | 487 |
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| Metapodatki: |    |
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