| Naslov: | On a definition of logarithm of quaternionic functions |
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| Avtorji: | ID Gentili, Graziano (Avtor)
ID Prezelj, Jasna (Avtor)
ID Vlacci, Fabio (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (425,44 KB)
MD5: CD7DEFECF052116C783ADEF9EA4908AF
 URL - Izvorni URL, za dostop obiščite https://ems.press/journals/jncg/articles/11806805
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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 a slice-regular quaternionic function $f$, the classical exponential function ${\mathrm exp} f$ is not slice-regular in general. An alternative definition of an exponential function, the $\ast$-exponential ${\mathrm exp}_\ast$, was given in the work by Altavilla and de Fabritiis (2019): if $f$ is a slice-regular function, then ${\mathrm exp}_\ast f$ is a slice-regular function as well. The study of a $\ast$-logarithm ${\mathrm log}_\ast f$ of a slice-regular function $f$ becomes of great interest for basic reasons, and is performed in this paper. The main result shows that the existence of such a ${\mathrm log}_\ast f$ depends only on the structure of the zero set of the vectorial part $f_v$ of the slice-regular function $f = f_0 + f_v$, besides the topology of its domain of definition. We also show that, locally, every slice-regular nonvanishing function has a $\ast$-logarithm and, at the end, we present an example of a nonvanishing slice-regular function on a ball which does not admit a $\ast$-logarithm on that ball. |
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| Ključne besede: | regular functions over quaternions, quaternionic logarithm of slice-regular functions |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2023 |
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| Leto izida: | 2023 |
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| Št. strani: | str. 1099-1128 |
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| Številčenje: | Vol. 17, no. 3 |
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| PID: | 20.500.12556/DiRROS-18648  |
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| UDK: | 517.5 |
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| ISSN pri članku: | 1661-6952 |
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| DOI: | 10.4171/JNCG/514 |
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| COBISS.SI-ID: | 162763779 |
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| Datum objave v DiRROS: | 10.04.2024 |
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| Število ogledov: | 62 |
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| Število prenosov: | 32 |
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| Metapodatki: |     |
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