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Advances in Applied Clifford Algebras

, Volume 22, Issue 4, pp 1109–1128 | Cite as

Normalized System for the Super Laplace Operator

  • Yuying Qiao
  • Hongfen Yuan
  • Heju Yang
Article

Abstract

In this paper, 0-normalized system for the super Laplace operator (that is Laplace operator in superspace) is established. According to this system, we obtain Almansi type decomposition of polyharmonic functions in superspace. Besides, we set up the relationship between the Riquier problem and the Dirichlet problem in superspace. In the end, the connection between harmonic functions and solutions to the Helmholtz equation in superspace is investigated.

Keywords

Superspace super Laplace operator normalized system Almansi type decomposition Riquier problem Helmholtz equation 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangP. R. China
  2. 2.College of ScienceHebei University of EngineeringHandanP. R. China
  3. 3.College of ScienceHebei University of Science and TechnologyShijiazhuangP. R. China

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