数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (2): 393-403.doi: 10.1016/S0252-9602(13)60006-5

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THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS

司中伟|杜金元   

  1. School of Mathematics and Information Science, Leshan Normal University, Leshan 614004, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2011-09-15 修回日期:2012-04-16 出版日期:2013-03-20 发布日期:2013-03-20
  • 基金资助:

    This work is supported by NNSF of China (11171260), RFDP of Higher Education of China (20100141110054), and Scientific Research Fund of Leshan Normal University (Z1265).

THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS

 SI Zhong-Wei, DU Jin-Yuan   

  1. School of Mathematics and Information Science, Leshan Normal University, Leshan 614004, China|School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2011-09-15 Revised:2012-04-16 Online:2013-03-20 Published:2013-03-20
  • Supported by:

    This work is supported by NNSF of China (11171260), RFDP of Higher Education of China (20100141110054), and Scientific Research Fund of Leshan Normal University (Z1265).

摘要:

Let R0,n be the real Clifford algebra generated by e1, e2, … , en satisfying eiej +ejei = −2δij , i, j = 1, 2, … , n. e0 is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation

Lf = 0, (0.1)
where
L = q0e0x0 + q1e1x1 + … + qnenxn,
qi > 0, i = 0, 1, … , n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn+1+ will be investigated.

关键词: Generalized analytic function, Hilbert boundary value problem, Hμ function

Abstract:

Let R0,n be the real Clifford algebra generated by e1, e2, … , en satisfying eiej +ejei = −2δij , i, j = 1, 2, … , n. e0 is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation

Lf = 0, (0.1)
where
L = q0e0x0 + q1e1x1 + … + qnenxn,
qi > 0, i = 0, 1, … , n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn+1+ will be investigated.

Key words: Generalized analytic function, Hilbert boundary value problem, Hμ function

中图分类号: 

  • 30G35