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

Let R-0,R-n be the real Clifford algebra generated by e(1), e(2), ... , e(n) satisfying e(i)e(j) + e(j)e(i) = -2 delta(ij), i, j, = 1, 2, ... ,n. e(0) is the unit element. Let Omega be an open set. A function f is called left generalized analytic in Omega if f satisfies the equation Lf = 0, where L = q(0)e(0)partial derivative(x0) + q(1)e(1)partial derivative(x1) + ... + q(n)e(n)partial derivative(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 R-+(n+1). will be investigated.