实轴上的双解析函数Riemann边值逆问题

The Inverse Riemann Boundary Value Problems for Bianalytic Functions on the Real Axis

提出了一类实轴上的双解析函数Riemann边值逆问题.先消去参变未知函数,再采用易于推广的矩阵形式记法,可把问题转化为两个实轴上的解析函数Riemann边值问题.利用经典的Riemann边值问题理论,讨论了该问题正则型情况的解法,得到了它的可解性定理.

A class of inverse Riemann boundary value problem for bianalytic functions on the real axis is proposed. By eliminating parametic unknown functions and using the notation of matrix form which will be generalized easily, the problem is transformed into two Riemann boundary value problems for analytic functions on the real axis. We discuss the solution of its normal case and obtain the theorem of its solvability according to the classical theory of Riemann boundary value problems.