On a definition of logarithm of quaternionic functions

  • Graziano Gentili

    Università di Firenze, Italy
  • Jasna Prezelj

    Univerza v Ljubljani; Univerza na Primorskem, Slovenia
  • Fabio Vlacci

    Università di Trieste, Italy
On a definition of logarithm of quaternionic functions cover
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For a slice-regular quaternionic function , the classical exponential function is not slice-regular in general. An alternative definition of an exponential function, the -exponential , was given in the work by Altavilla and de Fabritiis (2019): if is a slice-regular function, then is a slice-regular function as well. The study of a -logarithm of a slice-regular function becomes of great interest for basic reasons, and is performed in this paper. The main result shows that the existence of such a depends only on the structure of the zero set of the vectorial part of the slice-regular function , besides the topology of its domain of definition. We also show that, locally, every slice-regular nonvanishing function has a -logarithm and, at the end, we present an example of a nonvanishing slice-regular function on a ball which does not admit a -logarithm on that ball.

Cite this article

Graziano Gentili, Jasna Prezelj, Fabio Vlacci, On a definition of logarithm of quaternionic functions. J. Noncommut. Geom. 17 (2023), no. 3, pp. 1099–1128

DOI 10.4171/JNCG/514