A Kind of Hilbert Boundary Value Problem for Generalized Analytic Functions in Clifford Analysis

Abstract

Let R_0, n be the real Clifford algebra generated by e_1, e_2, cdots, e_n satisfying e_ie_j+e_je_i=-2 delta_ij for i, j=1, 2, cdots, n. e_0 is the unit element. In this paper, we first give the kernel function for the generalized analytic function. Further, a kind of Hilbert Boundary Value Problem for generalized analytic functions in R^n+1_+ will be investigated and the solution is obtained.