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Quantitative unique continuation principle for Schrödinger operators with singular potentials


Authors: Abel Klein and C. S. Sidney Tsang
Journal: Proc. Amer. Math. Soc. 144 (2016), 665-679
MSC (2010): Primary 35B99; Secondary 81Q10
DOI: https://doi.org/10.1090/proc12734
Published electronically: June 26, 2015
MathSciNet review: 3430843
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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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Additional Information

Abel Klein
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
Email: aklein@uci.edu

C. S. Sidney Tsang
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
Email: tsangcs@uci.edu

DOI: https://doi.org/10.1090/proc12734
Received by editor(s): August 8, 2014
Received by editor(s) in revised form: January 20, 2015
Published electronically: June 26, 2015
Additional Notes: Both authors were supported by the NSF under grant DMS-1301641.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2015 American Mathematical Society