By William Fulton

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1. 2) maps the space of all left monogenic functions defined on Sω◦ (Rn+1 ) bijectively onto the space of all C (Cn )-valued holomorphic functions defined on Sω◦ (Cn ). It is continuous between the compact-open topologies on each space. 8]. ψ : V ∩ Rn → C (Cn ) of two left monogenic functions defined in an open subset V of Rn+1 intersecting Rn ≡ {0} × Rn has a unique left monogenic extension φ · ψ to a neighbourhood of V ∩ Rn called the (left) Cauchy-Kowalewski product of φ and ψ. The following corollary shows that in the case V = Sω◦ (Rn+1 ), the product is actually defined on all of V .

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