The Analyticity for the Product of Analytic Functions on Octonions and Its Applications - Advances in Pure Mathematics

APM > Vol.7 No.12, December 2017

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

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Download as PDF (Size: 385KB) PP. 692-705

DOI: 10.4236/apm.2017.712043 789 Downloads 1,752 Views Citations

Author(s)

Jianquan Liao¹, Jinxun Wang²

Affiliation(s)

¹Department of Mathematics, Guangdong University of Education, Guangzhou, China.
²School of Finance, Guangdong University of Foreign Studies, Guangzhou, China.

ABSTRACT

Given two left O^c-analytic functions f, g in some open set Ω of R⁸, we obtain some sufficient conditions for fg is also left O^c-analytic in Ω. Moreover, we prove fλ 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.

KEYWORDS

Octonions, O^c-Analytic Functions, Stein-Weiss Conjugate Harmonic System, Cauchy-Kowalewski Product

Share and Cite:

Liao, J. and Wang, J. (2017) The Analyticity for the Product of Analytic Functions on Octonions and Its Applications. Advances in Pure Mathematics, 7, 692-705. doi: 10.4236/apm.2017.712043.

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