Acta mathematica scientia,Series B ›› 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

 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).

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

CLC Number: 

  • 30G35
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