PreprintCC BY-NC-ND 4.0arXiv
A connection between quaternionic slice regular and Fueter hyperholormorphic functions
Abstract
This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator G, Fueter operator 𝒟 and Laplacian operator Δℝ4. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball 𝔹4(0,1) given in terms of new series expansions of these functions.
Related
- A four-dimensional residue calculus for quaternionic slice regular functions
- Dual slice functions and dual quaternionic polynomials
- Quaternionic Möbius invariant Laplacian and quaternionic Möbius harmonic functions on the unit ball
- Hypothetical connection of the theta functions of Dirichlet characters with the real cyclotomic fields
- Holomorphic functions on complete Hermitian manifolds with flat Chern connection, II
BibTeX
@misc{gonzalezcervantes2026connection,
title = {{A connection between quaternionic slice regular and Fueter hyperholormorphic functions}},
author = {José Oscar González-Cervantes and Daniel González-Campos and Juan Bory-Reyes and Baruch Schneider},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.19496},
eprint = {2607.19496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.19496},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A connection between quaternionic slice regular and Fueter hyperholormorphic functions
AU - José Oscar González-Cervantes
AU - Daniel González-Campos
AU - Juan Bory-Reyes
AU - Baruch Schneider
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2607.19496
UR - https://arxiv.org/abs/2607.19496
AB - This paper presents some results for the slice regular functions and hyperholomorphic functions theories, as consequences of new relationships between the global operator G, Fueter operator 𝒟 and Laplacian operator Δ_ℝ^4. Although our results are presented in the quaternionic setting, a fine interpretation in terms of vector calculus of the slice regular function theory yields an interesting relationship between this theory and harmonic analysis. Moreover, we introduce and study a submodule of the hyperholomorphic functions associated to the unit ball 𝔹^4(0,1) given in terms of new series expansions of these functions.
ER -