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Given two left Oc-analytic functions f, g in some open set Ω of R8, we obtain some sufficient conditions for fg is also left Oc-analytic in Ω. Moreover, we prove fλ that is a left Oc-analytic function for any constants λ∈Oc if and only if is a complex Stein-Weiss conjugate harmonic system. Some applications and connections with Cauchy-Kowalewski product are also considered.

The Analyticity for the Product of Analytic Functions on Octonions and Its Applications