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St. Petersburg Mathematical Journal

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Absolutely continuous spectrum of a one-parameter family of Schrödinger operators


Author: O. Safronov
Original publication: Algebra i Analiz, tom 24 (2012), nomer 6.
Journal: St. Petersburg Math. J. 24 (2013), 977-989
MSC (2010): Primary 35J10
DOI: https://doi.org/10.1090/S1061-0022-2013-01275-1
Published electronically: September 23, 2013
MathSciNet review: 3097557
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Abstract: Under certain conditions on the potential $ V$, it is shown that the absolutely continuous spectrum of the Schrödinger operator $ -\Delta +\alpha V$ is essentially supported on $ [0,+\infty )$ for almost every $ \alpha \in \mathbb{R}$.


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Additional Information

O. Safronov
Affiliation: Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, North Carolina
Email: osafrono@uncc.edu

DOI: https://doi.org/10.1090/S1061-0022-2013-01275-1
Keywords: Schr\"odinger operator, spectral measure, Fourier transform, selfadjoint operator
Received by editor(s): June 7, 2011
Published electronically: September 23, 2013
Article copyright: © Copyright 2013 American Mathematical Society