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# Uniform resolvent estimates for Schrödinger operator with an inverse-square potential

 Mizutani, Haruya, Zhang, Junyong and Zheng, Jiqiang 2020. Uniform resolvent estimates for Schrödinger operator with an inverse-square potential. Journal of Functional Analysis 278 (4) , 108350. 10.1016/j.jfa.2019.108350

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## Abstract

We study the uniform resolvent estimates for Schr\'odinger operator with a Hardy-type singular potential. Let $\mathcal{L}_V=-\Delta+V(x)$ where $\Delta$ is the usual Laplacian on $\R^n$ and $V(x)=V_0(\theta) r^{-2}$ where $r=|x|, \theta=x/|x|$ and $V_0(\theta)\in\CC^1(\mathbb{S}^{n-1})$ is a real function such that the operator $-\Delta_\theta+V_0(\theta)+(n-2)^2/4$ is a strictly positive operator on $L^2(\mathbb{S}^{n-1})$. We prove some new uniform weighted resolvent estimates and also obtain some uniform Sobolev estimates associated with the operator $\mathcal{L}_V$.

Item Type: Article Publication Published Mathematics Elsevier 0022-1236 8 October 2019 01 Jul 2020 10:45 http://orca.cf.ac.uk/id/eprint/126141

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