Paracomplex Hermitean Clifford Analysis

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• 作者：Guangbin Ren (1)
  Haiyan Wang (1)
  Lin Chen (1)
  
• 关键词：Hermitean Clifford analysis ; Paracomplex numbers ; Witt basis ; Dirac operator ; Cauchy integral formula ; 30G35 ; 32A26
• 刊名：Complex Analysis and Operator Theory
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：8
• 期：6
• 页码：1367-1382
• 全文大小：211 KB
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  17. Price, G.B.: An Introduction to Multicomplex Spaces and Functions. Marcel Dekker, Inc., New York (1991)
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• 作者单位：Guangbin Ren (1)
  Haiyan Wang (1)
  Lin Chen (1)
  
  1. Department of Mathematics, University of Science and Technology of China, Hefei, 聽230026, China
  
• ISSN：1661-8262

文摘

Substituting the complex structure by the paracomplex structure plays an important role in para-geometry and para-analysis. In this article we shall introduce the paracomplex structure into the realm of Clifford analysis and establish paracomplex Hermitean Clifford analysis by constructing a paracomplex Hermitean Dirac operator \({\mathcal {D}}\) and establishing the corresponding Cauchy integral formula. The theory of paracomplex Hermitean Clifford analysis turns out to be similar to that of complex Hermitean Clifford analysis which recently emerged as a refinement of the theory of several complex variables. It deserves to be pointed out that the introduction of a single operator \({\mathcal {D}}\) in the paracomplex setting has an advantage over the complex setting where complex Hermitean monogenic functions are described by a system of equations instead of being given as null-solution of a single Dirac operator as in the case of classic monogenic functions.