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PreprintCC BY 4.0arXiv

Reconstruction of a slice regular function from some of its real components

  • Cinzia Bisi
  • Antonio Carbone
  • Riccardo Ghiloni
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Abstract

A basic property of holomorphic functions f:D→ ℂ defined on domains D of ℂ is that f is uniquely determined by its real part up to an additive constant. The same is true for slice regular functions defined on circular slice domains of the division algebra of quaternions or octonions. The aim of this paper is to extend the latter result to more general classes of algebras, including, among many others, the Clifford algebras ℝp,q and the split octonions 𝕊𝕆. New phenomena appear, as well as unexpected connections with graph theory and the theory of slice-Nash functions.

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Cite

BibTeXRIS
BibTeX
@misc{bisi2026reconstruction,
  title = {{Reconstruction of a slice regular function from some of its real components}},
  author = {Cinzia Bisi and Antonio Carbone and Riccardo Ghiloni},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04002},
  eprint = {2609.04002},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04002},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Reconstruction of a slice regular function from some of its real components
AU  - Cinzia Bisi
AU  - Antonio Carbone
AU  - Riccardo Ghiloni
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.04002
UR  - https://arxiv.org/abs/2609.04002
AB  - A basic property of holomorphic functions f:D→ ℂ defined on domains D of ℂ is that f is uniquely determined by its real part up to an additive constant. The same is true for slice regular functions defined on circular slice domains of the division algebra of quaternions or octonions. The aim of this paper is to extend the latter result to more general classes of algebras, including, among many others, the Clifford algebras ℝ_p,q and the split octonions 𝕊𝕆. New phenomena appear, as well as unexpected connections with graph theory and the theory of slice-Nash functions.
ER  -