复Banach空间中C-R方程的全纯解  

The Holomorphic Solutions of C-R Equations in Complex Banach Space

作　　者：龚昇[1] 刘太顺[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《数学学报（中文版）》2002年第1期1-6,共6页Acta Mathematica Sinica：Chinese Series

基　　金：973计划;国家自然科学基金(19971082; 19871081);安徽省自然科学基金资助项目

摘　　要：二重复数是复数的一种推广，在其上的全纯映照族对应于Ｃ２上满足复Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯映照族．可以证明，这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族．本文证明：即使在Ｂａｎａｃｈ空间中，Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯解，具有同样的性质．A commutative generalization of complex numbers is called bicomplex numbers. A holomorphic function of bicomplex number corresponds to a holomorphic mapping on C2 which satisfies the complex Cauchy-Riemann equations. It is known that the holomorphic solutions of complex Cauchy-Riemann equations are essentially the direct product of two holomorphic functions of one complex variable. In this short note, we prove that in the complex Banach space, the holomorphic solutions of the Cauchy-Riemann equations have the same property.

关 键 词：复BANACH空间 CAUCHY-RIEMANN方程 C2-全纯函数 T-全纯映照 全纯解 

分 类 号：O174.56[理学—数学]