The $$*$$-Exponential as a Covering Map-Reference-Cited by-同舟云学术

The $$*$$-Exponential as a Covering Map

Published:2024-08-17 Issue: Volume: Page:
ISSN:1617-9447
Container-title:Computational Methods and Function Theory
language:en
Short-container-title:Comput. Methods Funct. Theory

Author:

Altavilla Amedeo,Mongodi Samuele

Abstract

AbstractWe employ tools from complex analysis to construct the

$$*$$

∗ -logarithm of a quaternionic slice regular function. Our approach enables us to achieve three main objectives: we compute the monodromy associated with the

$$*$$

∗ -exponential; we establish sufficient conditions for the

$$*$$

∗ -product of two

$$*$$

∗ -exponentials to also be a

$$*$$

∗ -exponential; we calculate the slice derivative of the

$$*$$

∗ -exponential of a regular function.

Funder

Università degli Studi di Bari Aldo Moro

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s40315-024-00558-z.pdf

Reference15 articles.

1. Altavilla, A., de Fabritiis, C.: $$*$$-exponential of slice-regular functions. Proc. Am. Math. Soc. 147(3), 1173–1188 (2018). https://doi.org/10.1090/proc/14307

2. Altavilla, A., de Fabritiis, C.: s-regular functions which preserve a complex slice. Annali di Matematica Pura ed Applicata (1923 -) 197(4), 1269–1294 (2018). https://doi.org/10.1007/s10231-018-0724-1

3. Altavilla, A., de Fabritiis, C.: Equivalence of slice semi-regular functions via sylvester operators. Linear Algebra Appl. 607, 151–189 (2020). https://doi.org/10.1016/j.laa.2020.08.009

4. Altavilla, A., de Fabritiis, C.: $$*$$-logarithm for slice regular functions. Rendiconti Lincei, Matematica e Applicazioni 34(2), 491–529 (2023). https://doi.org/10.4171/rlm/1016

5. Altavilla, A., Mongodi, S.: Slice regular functions as covering maps and global $$\star $$-roots. J. Geom. Anal. 32(7), 207 (2022). https://doi.org/10.1007/s12220-022-00945-9