数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (3): 747-768.doi: 10.1016/S0252-9602(10)60076-8

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SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS

库敏1, 杜金2, 王道顺1   

  1. 1.Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China;
    2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2007-07-10 修回日期:2008-03-25 出版日期:2010-05-20 发布日期:2010-05-20
  • 基金资助:

    Supported by NNSF of China (6087349, 10871150), 863 Project of China  (2008AA01Z419), RFDP of Higher Education (20060486001), and Post-Doctor Foundation of China (20090460316)

SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS

 KU Min1, DU Jin-Yuan2, WANG Dao-Shun1   

  1. 1.Tsinghua National Laboratory for Information Science and Technology, \\
    Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China\\
    2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2007-07-10 Revised:2008-03-25 Online:2010-05-20 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)

摘要:

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.

关键词: Complex Clifford algebra, holomorphic Cliffordian functions, Taylor expansion, Laurent

Abstract:

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.

Key words: Complex Clifford algebra, holomorphic Cliffordian functions, Taylor expansion, Laurent

中图分类号: 

  • 22E30