SEMICLASSICAL RESOLVENT BOUNDS IN DIMENSION TWO

被引：13
|
作者：
Shapiro, Jacob [1 ]
机构：
[1] Univ Manchester, Sch Comp Sci, Kilburn Bldg,Oxford Rd, Manchester M13 9PL, Lancs, England
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 05期
关键词：
RESONANCES;
D O I：
10.1090/proc/13758
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give an elementary proof of weighted resolvent bounds for semiclassical Schrodinger operators in dimension two. We require the potential function to be Lipschitz with long range decay. The resolvent norm grows exponentially in the inverse semiclassical parameter, but near infinity it grows linearly. This result covers the missing case from the work of Datchev.
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页码：1999 / 2008
页数：10
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