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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Veröffentlicht in:	Acta mathematica scientia Jg. 30; H. 3; S. 747 - 768
1. Verfasser:	库敏杜金元王道顺
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	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
Schlagworte:	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-Zugang:	Volltext
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Zusammenfassung:	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.
Bibliographie:	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 ObjectType-Article-2 ObjectType-Feature-1
ISSN:	0252-9602 1572-9087
DOI:	10.1016/S0252-9602(10)60076-8