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Riemann slice-domains over quaternions II

Complex Variables 2018-09-26 v2

Abstract

We generalize the representation formula from slice-domains of regularity to general Riemann slice-domains. This result allows us to extend the *-product of slice regular functions on axially symmetric domains to certain Riemann slice-domains by introducing holomorphic stem systems and tensor holomorphic functions. In particular, we construct a power series expansions of slice regular functions on certain Riemann slice-domains, which implies a relation between stem holomorphic, tensor holomorphic and slice regular functions.

Keywords

Cite

@article{arxiv.1809.07979,
  title  = {Riemann slice-domains over quaternions II},
  author = {Xinyuan Dou and Guangbin Ren},
  journal= {arXiv preprint arXiv:1809.07979},
  year   = {2018}
}

Comments

49 pages

R2 v1 2026-06-23T04:13:39.601Z