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

 

Absolutely continuous spectrum of
perturbed Stark operators


Author: Alexander Kiselev
Journal: Trans. Amer. Math. Soc. 352 (2000), 243-256
MSC (1991): Primary 34L40, 81Q10
Published electronically: September 21, 1999
MathSciNet review: 1650105
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Abstract: We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark operator is stable if the perturbing potential decays at the rate $(1+x) ^{-\frac{1}{3}-\epsilon}$ or if it is continuously differentiable with derivative from the Hölder space $C_{\alpha}(R),$ with any $\alpha>0.$


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Additional Information

Alexander Kiselev
Affiliation: Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720
Address at time of publication: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637
Email: kiselev@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02450-2
PII: S 0002-9947(99)02450-2
Received by editor(s): April 14, 1997
Published electronically: September 21, 1999
Article copyright: © Copyright 1999 American Mathematical Society