| Title: | Reflexivity of the space of transversal distributions |
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| Authors: | ID Kališnik, Jure (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s12220-023-01390-y
 PDF - Presentation file, download (332,43 KB)
MD5: CE0285495983EE8EC68AB2CF5A861455
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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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| Keywords: | distributions with compact support, Fréchet spaces, transversal distributions, homomorphisms of modules, reflexive modules |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.10.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | 20 str. |
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| Numbering: | Vol. 33, iss. 10, article no. 331 |
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| PID: | 20.500.12556/DiRROS-18418  |
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| UDC: | 517.9 |
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| ISSN on article: | 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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| Note: |
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| Publication date in DiRROS: | 15.03.2024 |
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| Views: | 97 |
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| Downloads: | 44 |
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