上半平面中带平方根的Hilbert边值问题  

Hilbert Boundary Value Problem with Square Roots in the Upper Half-Plane

作　　者：史西专[1] 张利利[1] 

机构地区：[1]黄河科技学院信息工程学院,郑州450063

出　　处：《西南师范大学学报（自然科学版）》2017年第3期7-11,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：河南省科技计划项目(132300410217;142300410342)

摘　　要：讨论了上半平面中带平方根的Hilbert边值问题.先对未知函数进行结构分析,再把该问题转化为典型的上半平面中的Hilbert边值问题,然后通过关于实轴的对称扩张,将该问题进一步等价于实轴上的Riemann边值问题.利用已有结果得到了该问题的可解性定理.Hilbert boundary value problem with square roots in the upper half-plane has been discussed.By analyzing the structure of the unknown function,the problem has been transformed into a typical Hilbert boundary value problem in the upper half-plane.Then the problem is further equivalent to a kind of Riemann boundary value problem on the real axis by extension of symmetry with respect to the real axis.As a result,we establish the theorems of its solvability according to the known theory.

关 键 词：HILBERT边值问题 上半平面 RIEMANN边值问题 实轴 

分 类 号：O175.8[理学—数学]