SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

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 C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study p...

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Bibliographic Details
Published in:Acta mathematica scientia Vol. 30; no. 3; pp. 747 - 768
Main Author: 库敏 杜金元 王道顺
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.05.2010
Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China%School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
Subjects:
22E30
30G35
31C10
32A10
Algebra
Complex Clifford algebra
Complex variables
Foundations
holomorphic Cliffordian functions
Integrals
invariance
Laurent expansion
Lie groups
Mathematical analysis
Mathematics
Representations
Taylor expansion
代数函数
全纯函数
复变函数理论
多项式
子代数
定义值
表示公式
31C10
32A10
30G35
Taylor expansion
invariance
22E30
Laurent expansion
holomorphic Cliffordian functions
Complex Clifford algebra
ISSN:0252-9602, 1572-9087
Online Access:Get full text
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Description
Summary: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 C^n＋l, 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 holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.
Bibliography:O174.52
Complex Clifford algebra; holomorphic Cliffordian functions; Taylor expansion; Laurent exnansion;invariance
Taylor expansion
invariance
42-1227/O
holomorphic Cliffordian functions
O174.5
Laurent exnansion
Complex Clifford algebra
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
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ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(10)60076-8