Acta mathematica scientia, Series B >
SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS
Received date: 2007-07-10
Revised date: 2008-03-25
Online published: 2010-05-20
Supported by
Supported by NNSF of China (6087349, 10871150), 863 Project of China (2008AA01Z419), RFDP of Higher Education (20060486001), and Post-Doctor Foundation of China (20090460316)
In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D?mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.
KU Min , DU Jin-Yuan , WANG Dao-Shun . SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS[J]. Acta mathematica scientia, Series B, 2010 , 30(3) : 747 -768 . DOI: 10.1016/S0252-9602(10)60076-8
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