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.References
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Additional Information
- Abel Klein
- Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
- MR Author ID: 191739
- Email: aklein@uci.edu
- C. S. Sidney Tsang
- Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
- Email: tsangcs@uci.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 665-679
- MSC (2010): Primary 35B99; Secondary 81Q10
- DOI: https://doi.org/10.1090/proc12734
- MathSciNet review: 3430843