A local representation formula for quaternionic slice regular functions
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- by Graziano Gentili and Caterina Stoppato PDF
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Abstract:
After their introduction in 2006, quaternionic slice regular functions have mostly been studied over domains that are symmetric with respect to the real axis. This choice was motivated by some foundational results published in 2009, such as the Representation Formula for axially symmetric domains.
The present work studies slice regular functions over domains that are not axially symmetric, partly correcting the hypotheses of some previously published results. In particular, this work includes a Local Representation Formula valid without the symmetry hypothesis. Moreover, it determines a class of domains, called simple, having the following property: every slice regular function on a simple domain can be uniquely extended to the symmetric completion of its domain.
References
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Additional Information
- Graziano Gentili
- Affiliation: Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, I-50134 Firenze, Italy
- MR Author ID: 189767
- ORCID: 0000-0002-5001-2187
- Email: graziano.gentili@unifi.it
- Caterina Stoppato
- Affiliation: Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Viale Morgagni 67/A, I-50134 Firenze, Italy
- MR Author ID: 862712
- ORCID: 0000-0001-9859-6559
- Email: caterina.stoppato@unifi.it
- Received by editor(s): July 21, 2020
- Received by editor(s) in revised form: August 18, 2020
- Published electronically: March 2, 2021
- Additional Notes: This work was partly supported by INdAM, through: GNSAGA; INdAM project “Hypercomplex function theory and applications”. It was also partly supported by MIUR, through the projects: Finanziamento Premiale FOE 2014 “Splines for accUrate NumeRics: adaptIve models for Simulation Environments”; PRIN 2017 “Real and complex manifolds: topology, geometry and holomorphic dynamics”.
- Communicated by: Filippo Bracci
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 2025-2034
- MSC (2020): Primary 30G35; Secondary 32D05
- DOI: https://doi.org/10.1090/proc/15339
- MathSciNet review: 4232195