The hilbert boundary value problem for generalized analytic functions in clifford analysis

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 equation(0.1)Lf=0,Lf=0,where L=q0e0∂x0+ q1e1∂x1+…+qnen∂xn,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.