关于幅角原理及多值函数的讨论

DISCUSSION ON ARGUMENT PRINCIPLE AND MULTIVALUED FUNCTION

本文利用函数改变量和幅角函数改变量及其性质对幅角原理给以严格而又简捷的证明。同时对多值函数的单值分支问题进行了讨论,给出了多值函数可分出单值分支的充分条件,证明了较一般的单值性定理。

In this paper,The argument principle is proved strivtly and forthright by increment of a function and that of a argument as well as their properties. Mean while, the subject on the single-valued branch of a multivalued function is discussed, full conditions for the single-valued branch separated from a multivalued function are given,more,general monodromy theorems are proved.