| Naslov: | Quaternionic Cartan coverings and applications |
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| Avtorji: | ID Prezelj, Jasna (Avtor)
ID Vlacci, Fabio (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (582,39 KB)
MD5: A2733242690288AE8355B831C125CC65
 URL - Izvorni URL, za dostop obiščite https://link.springer.com/article/10.1007/s12220-025-01900-0
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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: | We present the topological foundations for solvability of multiplicative Cousin problems formulated on an axially symmetric domain $\Omega \subset {\mathbb H}$. In particular, we provide a geometric construction of quaternionic Cartan coverings, which are generalizations of (complex) Cartan coverings as presented in Section 4 of Forstnerič and Prezelj (Math. Ann. 322(4), 633-666 (2002)). Because of the requirements of symmetry inherent to the domains of definition of quaternionic regular functions, the existence of quaternionic Cartan coverings of $\Omega$ is not a consequence of the existence of complex Cartan coverings; for the latter, there are no requirements for the symmetries with respect to the real axis. Due to the real axis’s special role, also the covering restricted to $\Omega \cap {\mathbb R}$ must have additional properties. All these required properties were achieved by starting from a particular symmetric tiling of the symmetric set $\Omega \cap ({\mathbb R}+ i{\mathbb R})$. Finally, we apply these results to prove the vanishing of ’antisymmetric’ cohomology groups of planar symmetric domains for $n \ge 2$. |
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| Ključne besede: | quaternionic Cartan coverings, antisymmetric cohomology groups |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.03.2025 |
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| Leto izida: | 2025 |
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| Št. strani: | 25 str. |
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| Številčenje: | Vol. 35, iss. 3, [article no.] 80 |
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| PID: | 20.500.12556/DiRROS-21468  |
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| UDK: | 517.5 |
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| ISSN pri članku: | 1050-6926 |
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| DOI: | 10.1007/s12220-025-01900-0 |
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| COBISS.SI-ID: | 225630467 |
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| Datum objave v DiRROS: | 10.02.2025 |
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| Število ogledov: | 606 |
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| Število prenosov: | 297 |
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| Metapodatki: |    |
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