上半平面内的一类周期Hilbert边值逆问题

A Cycle Hilbert Boundary Value Inverse Problem on the Upper Half Plane

研究上半平面内具有间断系数的解析函数的周期Hilbert边值逆问题的数学提法,应用周期延拓、保形变换等方法将问题转化为Riemann边值问题,并据其理论,讨论了带有间断系数的Hilbert边值逆问题的可解性,给出了该类问题的可解条件及其在正则情况下的一般解.

In this paper we discuss mathematical definition of Hilbert boundary value inverse problem on the upper half plane with discontinuous coefficients,apply period prolongation and conformal transformation methods to convert the problem into Riemann boundary value problem,and according to the theory,discuss the solvability of the inverse Hilbert boundary value problem with discontinuous coefficients. We obtain the solvability conditions of the problem and its general solution in the case of regularq.