On a definition of logarithm of quaternionic functions

Gentili, Graziano (avtor), Prezelj, Jasna (avtor), Vlacci, Fabio (avtor)

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.

• Jezik: Angleški jezik
• Ključne besede: regular functions over quaternions, quaternionic logarithm of slice-regular functions
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.01.2023
• Leto izida: 2023
• Št. strani: Str. 1099-1128
• Številčenje: Vol. 17, no. 3
• PID: 20.500.12556/RUL-155646
• UDK: 517.5
• ISSN pri članku: 1661-6952
• DOI: 10.4171/JNCG/514
• COBISS.SI-ID: 162763779
• Datum objave v RUL: 10.04.2024

Gradivo je del revije

• Naslov: Journal of noncommutative geometry
• Skrajšan naslov: J. noncommut. geom.
• Založnik: EMS Publishing House, ETH-Zentrum FLI C4
• ISSN: 1661-6952
• COBISS.SI-ID: 17114713

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: regularne funkcije nad kvaternioni, logaritem, rezinsko regularne funkcije