Riemann Boundary Value Problems on the Sphere in Clifford Analysis

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• 作者：Min Ku (12) kumin0844@163.com
  Uwe K盲hler (1) ukaehler@ua.pt
  Daoshun Wang (2) daoshun@mail.tsinghua.edu.cn
• 关键词：Clifford analysis &#8211 ; generalized Cauchy ; Riemann operator &#8211 ; H枚lder continuous functions &#8211 ; sphere &#8211 ; Riemann boundary value problems
• 刊名：Advances in Applied Clifford Algebras
• 出版年：2012
• 出版时间：June 2012
• 年：2012
• 卷：22
• 期：2
• 页码：365-390
• 全文大小：410.3 KB
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• 作者单位：1. Centro de Investiga莽茫o e Desenvolvimento em Matem谩tica e Aplica莽玫es, Departamento de Matem谩tica, Universidade de Aveiro, P-3810-193 Aveiro, Portugal2. Department of Computer Science and Technology, Tsinghua University, Beijing, 100084 P.R. China
• 刊物类别：Physics and Astronomy
• 刊物主题：Mathematical Methods in Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Physics
  
• 出版者：Springer Basel
• ISSN：1661-4909

文摘

We present and study a type of Riemann boundary value problems (for short RBVPs) for polynomially monogenic functions, i.e. null solutions to polynomially generalized Cauchy-Riemann equations, over the sphere of \mathbbRn+1{\mathbb{R}^{n+1}}. Making use of Fischer type decomposition and the Clifford calculus for polynomially monogenic functions, we obtain explicit expressions of solutions of this kind of boundary value problems over the sphere of \mathbbRn+1{\mathbb{R}^{n+1}}. As special cases the solutions of the corresponding boundary value problems for classical polyanalytic functions and metaanalytic functions are derived respectively.