半平面中一类Riemann-Hilbert边值逆问题

A class of inverse Riemann-Hilbert boundary value problems in half plane

给出了半平面中一类解析函数的Riemann-Hilbert边值逆问题的数学提法,利用半平面中的Riemann-Hil-bert边值问题的已有结果,讨论了此边值逆问题在正则型和非正则型情况下的可解性,给出了其可解条件和解表达式.

The mathematical formulation of a class of inverse Riemann-Hilbert boundary value problems for analytic functions in half plane is given. On the basis of the classical theory of Riemann-Hilbert boundary value problems in half plane, the solvability of the inverse boundary value problems of the normal and non-normal cases are both discussed. The conditions and representations of the solutions are obtained.