上半平面内的周期Hilbert边值逆问题的研究

Inverse Hilbert boundary valueproblems on upper half-plane

给出了解析函数的周期Hilbert边值逆问题在上半平面内的数学提法,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,讨论了此类边值问题的可解性,给出了该类边值问题的可解条件及其在正则情况下的一般解.

In this paper,the mathematical formulation of the inverse Hilbert boundary value problems with periodicity of analytic function on upper half- plane was given. Transfered the problem into the Riemann boundary value problem by periodic continuation and conformal transform and so on. According to their classical theory,the solvability of the boundary value problems was discussed. And presented solvable conditions of this boundary value problems and general solve on the normal type.