TITLE:
The Analyticity for the Product of Analytic Functions on Octonions and Its Applications
AUTHORS:
Jianquan Liao, Jinxun Wang
KEYWORDS:
Octonions, Oc-Analytic Functions, Stein-Weiss Conjugate Harmonic System, Cauchy-Kowalewski Product
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.12,
December
26,
2017
ABSTRACT: 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 provefλ 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.