Riemann slice-domains over quaternions II

2018/09/21 by Xinyuan Dou, Dou, Xinyuan, Guangbin Ren +1
Mathematics · #30G35 (Primary) #32A30 #32D05 #32D26 (Secondary) #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CV #msc:30G35 #msc:32A30 #msc:32D05 #msc:32D26

paper · pdf · doi:10.48550/arxiv.1809.07979

49 pages

openalex publication_date 2018/09/21 · arxiv created 2018/09/25 · arxiv updated 2018/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Riemann slice-domains over quaternions I
• Extension theorem and representation formula in non-axially symmetric domains for slice regular functions
• Algebra of slice regular functions on non-symmetric domains in several quaternionic variables
• Path-slice star-product on non-axially symmetric domains in several quaternionic variables
• Domains of existence of slice regular functions in one quaternionic variable