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PreprintarXiv licencearXiv

Two-sided slice regular functions

  • Xinyuan Dou
  • Haosen Liu
  • Ting Yang*
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Abstract

In this paper, we introduce two types of two-sided slice regular functions, which are left slice regular in the first variable and right slice regular in the second variable. We prove that these two classes of functions coincide on axially symmetric domains. We further investigate fundamental properties of two-sided slice regular functions and define a star-product that preserves this regularity. In addition, we establish the Cauchy integral formula for these functions.

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Cite

BibTeXRIS
BibTeX
@misc{dou2026twosided,
  title = {{Two-sided slice regular functions}},
  author = {Xinyuan Dou and Haosen Liu and Ting Yang*},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05245},
  eprint = {2610.05245},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05245},
}
RIS
TY  - UNPB
TI  - Two-sided slice regular functions
AU  - Xinyuan Dou
AU  - Haosen Liu
AU  - Ting Yang*
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05245
UR  - https://arxiv.org/abs/2610.05245
AB  - In this paper, we introduce two types of two-sided slice regular functions, which are left slice regular in the first variable and right slice regular in the second variable. We prove that these two classes of functions coincide on axially symmetric domains. We further investigate fundamental properties of two-sided slice regular functions and define a star-product that preserves this regularity. In addition, we establish the Cauchy integral formula for these functions.
ER  -