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The Analyticity for the Product of Analytic Functions on Octonions and Its Applications
Department of Mathematics, Guangdong University of Education, Guangzhou, China
School of Finance, Guangdong University of Foreign Studies, Guangzhou, China
- 1 Department of Mathematics, Guangdong University of Education, Guangzhou, China
- 2 School of Finance, Guangdong University of Foreign Studies, Guangzhou, China
Advances in Pure Mathematics·Volume 07 (2017)·Pages 692–705·Published 11 December 2017·DOI10.4236/apm.2017.712043
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Abstract
Given two left O c -analytic functions f , g in some open set Ω of R 8 , we obtain some sufficient conditions for fg is also left O c -analytic in Ω . Moreover, we prove f λ that is a left O c -analytic function for any constants λ ∈ O c if and only if is a complex Stein - Weiss conjugate harmonic system. Some applications and connections with Cauchy- Kowalewski product are also considered.
KeywordsOctonions<b>O</b><sup>c</sup>-Analytic FunctionsStein-Weiss Conjugate Harmonic SystemCauchy-Kowalewski Product
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