Quantitative unique continuation principle for Schrödinger operators with singular potentials

Klein, Abel; Tsang, C.

doi:10.1090/proc12734

Quantitative unique continuation principle for Schrödinger operators with singular potentials
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by Abel Klein and C. S. Sidney Tsang PDF

Proc. Amer. Math. Soc. 144 (2016), 665-679 Request permission

Abstract:

We prove a quantitative unique continuation principle for Schrödinger operators $H=-\Delta +V$ on $\mathrm {L}^2(\Omega )$, where $\Omega$ is an open subset of $\mathbb {R}^d$ and $V$ is a singular potential: $V \in \mathrm {L}^\infty (\Omega ) + \mathrm {L}^p(\Omega )$. As an application, we derive a unique continuation principle for spectral projections of Schrödinger operators with singular potentials.

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