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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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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