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On a definition of logarithm of quaternionic functionsGentili, Graziano ; Prezelj, Jasna ; Vlacci, FabioFor 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.Source: Journal of noncommutative geometry. - ISSN 1661-6952 (Vol. 17, no. 3, 2023, str. 1099-1128)Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 162763779
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Author | Gentili, Graziano ; Prezelj, Jasna ; Vlacci, Fabio |
Title | On a definition of logarithm of quaternionic functions |
Publication date | 2023-01-01 |
COBISS.SI-ID | 162763779 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution 4.0 International |
Embargo | Immediate publication for public |
Project(s) from which the publication was funded
Title | Acronym | Project ID | Funder |
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Analiza in geometrija | P1-0291-2022 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
|
Kompleksna in geometrijska analiza | J1-3005-2021 |
Javna agencija za znanstvenoraziskovalno in inovacijsko dejavnost Republike Slovenije |
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Gentili, Graziano | ![]() |
Prezelj, Jasna | 20821 |
Vlacci, Fabio | 52453 |
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