锥中与稳态的薛定谔算子相关的广义Martin函数无穷远处的控制（英文）  

MAJORIZATION OF THE GENERALIZED MARTIN FUNCTIONS FOR THE STATIONARY SCHR?DINGER OPERATOR AT INFINITY IN A CONE

作　　者：龙品红[1] 韩惠丽[1] LONG Pin-hong HAN Hui-li(School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学数学计算机学院,宁夏银川750021

出　　处：《数学杂志》2017年第1期51-62,共12页Journal of Mathematics

基　　金：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

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.In the paper, we mainly study Dirichlet problem for the stationary Schrdinger operator and the boundary behavior of Martin function. Depended on the generalized Martin representation and the fundamental system of solutions of an ordinary differential equation corresponding to stationary Schrdinger operator, we obtain some characterizations for the majorization of the generalized Martin functions associated with the stationary Schrdinger operator in a cone with smooth boundary, and generalize some classical results in Laplace setting.

关 键 词：稳态的薛定谔算子 Martin函数 调和控制 极细 锥 

分 类 号：O174.3[理学—数学]