双解析函数Schwarz问题的2种新解法

Two New Solutions of Schwarz Problem of Bi-analytic Functions

利用2种方法去寻求单位圆上双解析函数的Schwarz问题的解:一是对双解析函数的Schwarz问题分解后再求解;二是先把双解析函数的Schwarz问题转化为解析函数的Schwarz问题,然后再求解;2种解法都得到了解的积分表示,并得到了双解析函数的Hilbert公式。

Two methods were used to seek the solution of Schwarz problem of bi-analytic functions on the unit circle.The problem was solved by decomposing the Schwarz problem of bi-analytic functions.Meanwhile,the original problem was solved by turning the Schwarz problem of bi-analytic functions into Schwarz problem of analytic functions.The integral formula of the solution was obtained by the two methods,and the Hilbert formula of bi-analytic functions was also got.