数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1419-1430.doi: 10.1016/S0252-9602(13)60093-4

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GAUSS-MEAN VALUE FORMULA FOR TRIHARMONIC FUNCTIONS AND ITS APPLICATIONS IN CLIFFORD ANALYSIS

谷龙飞|张忠祥   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2011-07-26 修回日期:2013-03-04 出版日期:2013-09-20 发布日期:2013-09-20
  • 通讯作者: glfcool@163.com E-mail:glfcool@163.com;zhangzx9@sohu.com
  • 基金资助:

    Research supported by NNSF for Young Scholars of China(11001206).

GAUSS-MEAN VALUE FORMULA FOR TRIHARMONIC FUNCTIONS AND ITS APPLICATIONS IN CLIFFORD ANALYSIS

 GU Long-Fei, ZHANG Zhong-Xiang   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2011-07-26 Revised:2013-03-04 Online:2013-09-20 Published:2013-09-20
  • Contact: glfcool@163.com E-mail:glfcool@163.com;zhangzx9@sohu.com
  • Supported by:

    Research supported by NNSF for Young Scholars of China(11001206).

摘要:

In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl(Vn,n) is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl(Vn,n) are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.

关键词: triharmonic function, Clifford algebra, Gauss-mean value formula

Abstract:

In this paper, the integral representation for some polyharmonic functions with values in a universal Clifford algebra Cl(Vn,n) is studied and Gauss-mean value formula for triharmonic functions with values in a Clifford algebra Cl(Vn,n) are proved by using Stokes formula and higher order Cauchy-Pompeiu formula. As application some results about growth condition at infinity are obtained.

Key words: triharmonic function, Clifford algebra, Gauss-mean value formula

中图分类号: 

  • 30G35