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

作　　者：Jianquan Liao Jinxun Wang 

机构地区：[1]Department of Mathematics, Guangdong University of Education, Guangzhou, China [2]School of Finance, Guangdong University of Foreign Studies, Guangzhou, China

出　　处：《Advances in Pure Mathematics》2017年第12期692-705,共14页理论数学进展（英文）

摘　　要：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.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.

关 键 词：OCTONIONS Oc-Analytic Functions Stein-Weiss Conjugate Harmonic System Cauchy-Kowalewski PRODUCT 

分 类 号：O1[理学—数学]