多Clifford分析的Cauchy-Riemann方程  

The Cauchy-Riemann equation in Clifford analysis of several variables

作　　者：王海燕[1] Haiyan Wang

机构地区：[1]天津职业技术师范大学理学院,天津300222

出　　处：《中国科学：数学》2018年第2期281-288,共8页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11601390和11526154);天津职业技术师范大学校级项目(批准号:KYQD14041和KJ15-18)资助项目

摘　　要：多Clifford变量的分析理论是多复变函数论在非交换领域的推广.本文给出了非齐次Cauchy-Riemann方程具有紧支集解的微分相容条件及解的具体积分表达式,并证明了多Clifford分析理论中的正则函数具有Hartogs现象.这些结果将推广多复变中相应结果.The aim of this article is to extend the theory of several complex variables to the non-commutative realm. In this paper, we solve the non-homogeneous Cauchy-Riemann equation under the differential compatibility condition, find the explicit integral representation of the solution and derive the Hartogs theorem in Clifford analysis of several variables. This will generalize the corresponding results in several complex variables.

关 键 词：多变量Clifford分析 CAUCHY-RIEMANN方程 微分相容条件 

分 类 号：O175[理学—数学]