双解析函数的Riemann边值逆问题

给出双解析函数的一类Riemann边值逆问题正则型与非正则型情况的提法。基于双解析函数的正则型Riemann边值问题,讨论了双解析函数Riemann边值逆问题正则型情况的可解性,得到了该边值逆问题的可解性结论：当问题的指标κ≥0时,该边值逆问题具有2κ 1个线性无关解;当指标κ＜0时,该边值逆问题只有零解,即双解析函数的正则型Riemann边值逆问题的一般解具有2κ 1个自由度。

The Inverse Riemann Boundary Value Problems for Bianalytic Functions

A formulation of a class of inverse Riemann boundary value problems for bianalytic functions is proposed, its normal and nonnormal cases are also proposed. On the basis of the Riemann boundary value problems of normal case for bianalytic functions, the solvability of the inverse Riemann boundary value problems of normal case for bianalytic functions is discussed, and the theorems of solvability of the problems are obtained:the problems possess 2κ+1 linearly independent solutions when its index κ0; it only possesses zero-solution when the index κ＜0. In a word, the general solution of the problems has 2κ+1 degree of freedom.