Generalized integral representations in Clifford analysis - Begehr, Heinrich; Zhongxiang, Zhang; Ngoc Ha, Vu Thi (Complex variables and elliptic equations, 2006)
Based on the solution of the Helmholtz equation in this article, we get the generalized Cauchy integral formula, the Cauchy-Pompeiu formula, the higher-order Cauchy-Pompeiu formula, and the generalized integral representations related with the Helmholtz operator for functions with values in a universal Clifford algebra C(V n ,n). We also give weak solutions of the inhomogeneous equations L k u = f and , k ≥ 1, where Lu=Du+uh and , D is the Dirac operator. §Dedicated to Professor Guochun Wen on the occasion of his 75th birthday.