边界过原点的任意半平面中的Hilbert边值问题

Hilbert Boundary Value Problem on Arbitrary Half-Plane with Its Boundary Passing Through the Origin

给出了边界过原点的任意半平面中的Hilbert边值问题的提法,定义了函数的一种对称扩张,并利用这种对称扩张将此Hilbert边值问题转化为无穷直线上的Riemann边值问题,得到了该问题的一般解和可解性定理.

The formulation of Hilbert boundary value problem on arbitrary half-plane with its boundary passing through the origin was proposed. And one kind of symmetric extending of function was defined, then by means of this symmetric extending of function, the Hilbert boundary value problem was reduced to the Riemann boundary value problem on infinite straight line, then the solvability of the problems was discussed, and the general solutions and the theorems of solvability of the problem were obtained .