| Title: | On a definition of logarithm of quaternionic functions |
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| Authors: | ID Gentili, Graziano (Author)
ID Prezelj, Jasna (Author)
ID Vlacci, Fabio (Author) |
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| Files: |  PDF - Presentation file, download (425,44 KB)
MD5: CD7DEFECF052116C783ADEF9EA4908AF
 URL - Source URL, visit https://ems.press/journals/jncg/articles/11806805
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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 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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| Keywords: | regular functions over quaternions, quaternionic logarithm of slice-regular functions |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 1099-1128 |
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| Numbering: | Vol. 17, no. 3 |
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| PID: | 20.500.12556/DiRROS-18648  |
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| UDC: | 517.5 |
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| ISSN on article: | 1661-6952 |
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| DOI: | 10.4171/JNCG/514 |
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| COBISS.SI-ID: | 162763779 |
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| Publication date in DiRROS: | 10.04.2024 |
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| Views: | 1014 |
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| Downloads: | 556 |
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