无穷远点处与Schr?dinger算子相关的极细集  

Minimally thin sets at infinity with respect to the Schr?dinger operator

作　　者：乔蕾[1] 邓冠铁[2] 

机构地区：[1]河南财经政法大学数学与信息科技学院,郑州450046 [2]北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京100875

出　　处：《中国科学：数学》2014年第12期1247-1256,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11271045,U1304102和11301140);河南省教育厅科学技术指导计划资助项目(批准号:13A110036和12B110001);河南省科技厅科技攻关科学基金(批准号:112102310519)资助项目

摘　　要：本文首先得到了一些新的关于锥中无穷远点处与Schr?dinger算子相关极细集的判定准则,其证明是基于对带有修改测度的Green-Sch位势在无穷远点处渐近行为的估计.接着,刻画了这类极细集的几何性质.最后,通过一个反例来说明,所得几何性质的逆命题并不成立.This paper gives some criterions for minimally thin sets at infinity with respect to the SchrSdinger operator in a cone. Our proofs are based on estimating Green-Sch potential with a positive measure by connecting with a kind of density of the modified measure. Meanwhile, the geometrical property of this minimally thin sets at infinity is also considered. By giving an example, we show that the reverse of this property is not true.

关 键 词：极细集 SCHRODINGER算子 Green-Sch位势 

分 类 号：O177[理学—数学] O144[理学—基础数学]