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Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems

  • Cinzia Bisi
  • Joerg Winkelmann
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Abstract

Slice regular functions are a generalization of holomorphic functions where alternative real *-algebras are considered instead of the field of complex numbers. For such functions we show that zero sets and function values on suitable subsets may be prescribed. As a consequence, we show that for any axially symmetric domain there exist slice regular functions which (due to the nature of its zero set) can not be extended to a larger such domain.

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Cite

BibTeXRIS
BibTeX
@misc{bisi2026slice,
  title = {{Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems}},
  author = {Cinzia Bisi and Joerg Winkelmann},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06160},
  eprint = {2609.06160},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06160},
}
RIS
TY  - UNPB
TI  - Slice regular functions on alternative *-algebras : prescribing zeroes and values on discrete sets and related extension problems
AU  - Cinzia Bisi
AU  - Joerg Winkelmann
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2609.06160
UR  - https://arxiv.org/abs/2609.06160
AB  - Slice regular functions are a generalization of holomorphic functions where alternative real *-algebras are considered instead of the field of complex numbers. For such functions we show that zero sets and function values on suitable subsets may be prescribed. As a consequence, we show that for any axially symmetric domain there exist slice regular functions which (due to the nature of its zero set) can not be extended to a larger such domain.
ER  -