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Title:On a definition of logarithm of quaternionic functions
Authors:ID Gentili, Graziano (Author)
ID Prezelj, Jasna (Author)
ID Vlacci, Fabio (Author)
Files:.pdf PDF - Presentation file, download (425,44 KB)
MD5: CD7DEFECF052116C783ADEF9EA4908AF
 
URL URL - Source URL, visit https://ems.press/journals/jncg/articles/11806805
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract:For a slice-regular quaternionic function f, the classical exponential function expf is not slice-regular in general. An alternative definition of an exponential function, the ∗-exponential exp∗, was given in the work by Altavilla and de Fabritiis (2019): if f is a slice-regular function, then exp∗f is a slice-regular function as well. The study of a ∗-logarithm log∗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 log∗f depends only on the structure of the zero set of the vectorial part fv of the slice-regular function f=f0+fv, 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.
Keywords:regular functions over quaternions, quaternionic logarithm of slice-regular functions
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2023
Year of publishing:2023
Number of pages:str. 1099-1128
Numbering:Vol. 17, no. 3
PID:20.500.12556/DiRROS-18648 New window
UDC:517.5
ISSN on article:1661-6952
DOI:10.4171/JNCG/514 New window
COBISS.SI-ID:162763779 New window
Publication date in DiRROS:10.04.2024
Views:642
Downloads:285
Metadata:XML DC-XML DC-RDF
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GENTILI, Graziano, PREZELJ, Jasna and VLACCI, Fabio, 2023, On a definition of logarithm of quaternionic functions. Journal of noncommutative geometry [online]. 2023. Vol. 17, no. 3, p. 1099–1128. [Accessed 9 April 2025]. DOI 10.4171/JNCG/514. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=18648
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Record is a part of a journal

Title:Journal of noncommutative geometry
Shortened title:J. noncommut. geom.
Publisher:EMS Publishing House, ETH-Zentrum FLI C4
ISSN:1661-6952
COBISS.SI-ID:17114713 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0291-2022
Name:Analiza in geometrija
Funder:ARRS - Slovenian Research Agency
Project number:J1-3005-2021
Name:Kompleksna in geometrijska analiza
Funder:Other - Other funder or multiple funders
Funding programme:INdAM, National Group for Mathematical Analysis, Probability and their Applications (GNAMPA)
Name:Hypercomplex function theory and applications
Funder:Other - Other funder or multiple funders
Funding programme:MIUR, Italy
Project number:Finanziamento Premiale FOE 2014
Name:Splines for accUrate NumeRics: adaptIve models for Simulation Environments
Funder:Other - Other funder or multiple funders
Funding programme:PRIN 2017
Name:Real and complex manifolds: topology, geometry and holomorphic dynamics

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:regularne funkcije nad kvaternioni, logaritem, rezinsko regularne funkcije


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