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

【摘要】 Let R0,n be the real Clifford algebra generated by e1 , e2 , ··· , en satisfying ei ej + ej ei =-2δij , i,j = 1,2, ··· , n. e0 is the unit element. Let be an open set. A function f is called left generalized analytic in if f satisfies the equation Lf = 0, (0.1) where L = q0e0 θx0+q1e1θx1+ ··· + qn e nθxn , 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.更多还原

【Abstract】 Let R0,n be the real Clifford algebra generated by e1 , e2 , · · · , en satisfying ei ej + ej ei =-2δij , i,j = 1,2, · · · , n. e0 is the unit element. Let be an open set. A function f is called left generalized analytic in if f satisfies the equation Lf = 0, (0.1) where L = q0e0 θx0+q1e1θx1+ · · · + qn e nθxn , 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.更多还原