20.500.12556/DiRROS-18648 On a definition of logarithm of quaternionic functions 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. regular functions over quaternions quaternionic logarithm of slice-regular functions regularne funkcije nad kvaternioni logaritem rezinsko regularne funkcije true false true Angleški jezik Slovenski jezik Neznano 2024-04-10 08:26:19 2024-04-10 08:26:20 2024-04-11 03:34:32 0000-00-00 00:00:00 2023 0 0 str. 1099-1128 no. 3 Vol. 17 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2023-01-01 517.5 1661-6952 10.4171/JNCG/514 162763779 10.4171-jncg-514.pdf 10.4171-jncg-514.pdf 1 CD7DEFECF052116C783ADEF9EA4908AF 1557c4762fbdc42fc4e5bdb832c518d8869aca3b3da55715ba64eb9cb8ce8524 82965ae6-f6f2-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25473 https://ems.press/journals/jncg/articles/11806805 1 7bd7c777-f6f2-11ee-ae20-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=25472 Inštitut za matematiko, fiziko in mehaniko 0 0 0