Generalized integral representations in Clifford analysis

• Published in: Complex variables and elliptic equations Vol. 51; no. 8-11; pp. 745 - 762
• Main Authors: Begehr, Heinrich, Zhongxiang, Zhang, Ngoc Ha, Vu Thi
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.08.2006
• Subjects: 2000 MR Subject Classifications: 30G35; Helmholtz equation; Higher-order Cauchy-Pompeiu formula; Universal Clifford algebra
• ISSN: 1747-6933; 1747-6941
• DOI: 10.1080/17476930600672940

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.