The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-ho...The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11371337)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20123402110068)
文摘The aim of this article is to extend the theory of several complex variables to the non-commutative realm. Some basic results,such as the Bochner-Martinelli formula,the existence theorem of the solutions to the non-homogeneous Cauchy-Riemann equations,and the Hartogs theorem,are generalized from complex analysis in several variables to Clifford analysis in several paravector variables. In particular,the Bochner-Martinelli formula in several paravector variables unifies the corresponding formulas in the theory of one complex variable,several complex variables,and several quaternionic variables with suitable modifications.
