Acta mathematica scientia, Series B >
THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS
Received date: 2011-09-15
Revised date: 2012-04-16
Online 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).
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 = q0e0∂x0 + q1e1∂x1 + … + qnen∂xn,
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.
SI Zhong-Wei , DU Jin-Yuan . THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS[J]. Acta mathematica scientia, Series B, 2013 , 33(2) : 393 -403 . DOI: 10.1016/S0252-9602(13)60006-5
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