VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • On a definition of logarithm of quaternionic functions
    Gentili, Graziano ; Prezelj, Jasna ; Vlacci, Fabio
    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.
    Vir: Journal of noncommutative geometry. - ISSN 1661-6952 (Vol. 17, no. 3, 2023, str. 1099-1128)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 162763779

    Povezava(-e):

    https://ems.press/journals/jncg/articles/11806805
    Repozitorij Univerze v Ljubljani – RUL
    DiRROS - Digitalni repozitorij raziskovalnih organizacij Slovenije
    DOI

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