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| 上半平面中含参变未知函数的Hilbert边值问题 | |
| 引用本文： | 曹丽霞,李平润,孙平. 上半平面中含参变未知函数的Hilbert边值问题[J]. 数学的实践与认识, 2012, 42(2): 189-194 |
| 作者姓名： | 曹丽霞 李平润 孙平 |
| 作者单位： | 1. 东北石油大学数学科学与技术学院,黑龙江大庆,163318 2. 曲阜师范大学数学科学学院,山东曲阜,273165 3. 沈阳建筑大学理学院,辽宁沈阳,110168 |
| 摘 要： | 给出了上半平面中的含参变未知函数的Hilbert边值问题的提法,利用函数的对称扩张,将其转化为无穷直线上含参变未知函数的Riemann边值问题,得到了该问题的一般解和可解性定理. |
| 关 键 词： | 上半平面 参变未知函数 Hilbert边值问题 Riemann边值问题 可解性 |
The Hilbert Boundary Value Problem with Parametric Unknown Function on Upper Half-plane |
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| CAO Li-xia , LI Ping-run , SUN Ping. The Hilbert Boundary Value Problem with Parametric Unknown Function on Upper Half-plane[J]. Mathematics in Practice and Theory, 2012, 42(2): 189-194 | |
| Authors: | CAO Li-xia LI Ping-run SUN Ping |
| Affiliation: | 1.Mathematics College,Northeast Petroleum University,Daqing 163318,China) (2.Shool of Mathematical Sciences,Qufu Normal University,Qufu 273165,China) (3.The School of Science,Shenyang Jianzhu University,Shenyang 110168,China) |
| Abstract: | The formulation of Hilbert boundary value problem with parametric unknown function on upper half-plane was proposed.By means of the symmetric extending of function, this problem was reduced to the Riemann boundary value problem with parametric unknown function on infinite straight line,then the solvability of the problem was discussed,and the general solutions and the theorems of solvability of the problem were obtained. |
| Keywords: | upper half-plane parametric unknown function Hilbert boundary value problem Riemann boundary value problem solvability |
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