具有间断系数的周期Hilbert边值问题

The Periodic Hilbert Boundary Value Problem with Discontinuous Coefficient

本文给出了单位圆和上半平面两种情况下的带有间断系数的周期Hilbert边值问题的提法,并应用周期延拓、保形变换等方法将其转化为经典的Riemann边值问题和Hilbert边值问题,从而得出正则型情况下的一般解.

In this paper,we give the expressions of the periodic Hilbert boundary value problem on unit disk or upper half-plane with discontinuous coefficient, then transfer the problem into the general Riemann boundary value problem andHilbert boundary value problem by period continuation and conformaltransform. At last we get the general solve on regular type.