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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Resonances for steplike potentials: Forward and inverse results


Author: T. Christiansen
Journal: Trans. Amer. Math. Soc. 358 (2006), 2071-2089
MSC (2000): Primary 34L25, 34A55, 81U40, 81U05
Published electronically: March 31, 2005
MathSciNet review: 2197448
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Abstract: We consider resonances associated to the one dimensional Schrödinger operator $-\frac{d^2}{dx^2}+V(x)$, where $V(x)=V_+$ if $x>x_M$ and $V(x)=V_-$ if $x<-x_M$, with $V_+\not = V_-$. We obtain asymptotics of the resonance-counting function for several regions. Moreover, we show that in several situations, the resonances, $V_+$, and $V_-$ determine $V$ uniquely up to translation.


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Additional Information

T. Christiansen
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: tjc@math.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-05-03716-5
PII: S 0002-9947(05)03716-5
Keywords: Steplike potentials, Schr\"odinger operator, resonances, inverse problem
Received by editor(s): March 4, 2003
Received by editor(s) in revised form: March 31, 2004
Published electronically: March 31, 2005
Additional Notes: This work was partially supported by NSF grant 0088922.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.