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| 摘要: |
| 本文研究了稳态的薛定谔算子的Dirichlet问题和Martin函数的边界行为.利用广义Martin表示和稳态的薛定谔算子对应的常微分方程基本解，在具有光滑边界的锥形区域中获得了与稳态的薛定谔算子相关的广义Martin函数无穷远处广义调和控制的一些刻画，推广了拉普拉斯算子情形的结果. |
| 关键词: 稳态的薛定谔算子 Martin函数 调和控制 极细 锥 |
| DOI： |
| 分类号:O174.3 |
| 基金项目:Supported by National Natural Science Foundation of China (11271045; 11261041); Natural Science Foundation of Ningxia University (NDZR1301); Startup Foundation for Doctor Scientific Research of Ningxia University. |
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| MAJORIZATION OF THE GENERALIZED MARTIN FUNCTIONS FOR THE STATIONARY SCHRÖDINGER OPERATOR AT INFLNITY IN A CONE |
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LONG Pin-hong,HAN Hui-li
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| Abstract: |
| In the paper, we mainly study Dirichlet problem for the stationary Schrödinger operator and the boundary behavior of Martin function. Depended on the generalized Martin representation and the fundamental system of solutions of an ordinary difierential equation corresponding to stationary Schrödinger operator, we obtain some characterizations for the majorization of the generalized Martin functions associated with the stationary Schrödinger operator in a cone with smooth boundary, and generalize some classical results in Laplace setting. |
| Key words: stationary Schrödinger operator Martin function harmonic majorization minimally thin cone |
