实Clifford分析中双正则函数的一些性质

Some Properties of Biregular Functions in Real Clifford Analysis

研究了含有2个变量的正则函数,所谓的双正则函数.正则函数是单复分析中全纯函数在高维空间的推广,全纯函数的经典函数理论如Morera定理,开拓定理等都可推广到正则函数,同样也可推广到双正则函数.以双正则函数的柯西积分公式为基础,得到了双正则函数的Morera定理,开拓定理,平均值定理.

The regular functions with two variables are studied,so called biregular functions. Biregular functions are the extension of regular functions in high dimensional space. The classical theorems of analytic functions of one complex variable such as Morera theoremand painleve theorem are generalized to regular functions,similarly to biregular functions. Therefore, Morera theorem, painleve theorem and mean value theorem for biregular functions based on Cauchy integral formula are obtained.