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arxiv: 1809.07979 · v2 · pith:HF3F33SUnew · submitted 2018-09-21 · 🧮 math.CV

Riemann slice-domains over quaternions II

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keywords slice-domainsfunctionsholomorphicriemannregularslicecertainstem
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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.

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