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

作　　者：司中伟 杜金元 

机构地区：[1]School of Mathematics and Information Science,Leshan Normal University [2]School of Mathematics and Statistics,Wuhan University

出　　处：《Acta Mathematica Scientia》2013年第2期393-403,共11页数学物理学报（B辑英文版）

基　　金：supported by NNSF of China (11171260);RFDP of Higher Education of China (20100141110054);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…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 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.Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 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 H^u function 

分 类 号：O175.8[理学—数学] O174.55[理学—基础数学]