单位圆周上的周期Hilbert边值逆问题的研究

Research into the Inverse Problems of Hilbert Boundary Value on Unit Circles with Periodicity

文章介绍了解析函数的周期Hilbert边值逆问题在单位圆周上的数学提法,应用周期延拓、保形变换等方法将问题转化为经典的Riemann边值问题和Hilbert边值问题,并依据它们的经典理论,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。

This paper gives the mathematical formulation of the inverse problems of Hilbert boundary value with periodicity of analytic function on the unit circle and then transfers the problem into the classical Riemann boundary value problem and Hilbert boundary value problem by periodic continuation and conformal transform and so on. According to their classical theory, the solvability of the boundary value problems is discussed and the solvable conditions of this boundary value problems and general solutions on the normal type are presented.