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Semiclassical resolvent bound for compactly supporte $L^\infty$ potentials
Journal of Spectral Theory ( IF 1.0 ) Pub Date : 2020-05-22 , DOI: 10.4171/jst/308
Jacob Shapiro 1
Affiliation  

We give an elementary proof of a weighted resolvent estimate for semiclassical Schrödinger operators in dimension $n \ge 1$. We require the potential belong to $L^\infty(\mathbb{R}^n)$ and have compact support, but do not require that it have distributional derivatives in $L^\infty(\mathbb{R}^n)$. The weighted resolvent norm is bounded by $e^{Ch^{-4/3}\log(h^{-1})}$, where $h$ is the semiclassical parameter.

中文翻译:

半经典分解物必将紧紧支撑$ L ^ \ infty $势

我们给出维度为$ n \ ge 1 $的半经典Schrödinger算子的加权分解估计的初等证明。我们要求势能属于$ L ^ \ infty(\ mathbb {R} ^ n)$并具有紧凑支持,但不要求其在$ L ^ \ infty(\ mathbb {R} ^ n)中具有分布导数$。加权分解范数以$ e ^ {Ch ^ {-4/3} \ log(h ^ {-1})} $为界,其中$ h $是半经典参数。
更新日期:2020-07-20
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