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On the singular spectrum of Schrödinger operators with decaying potential


Authors: S. Denisov and S. Kupin
Journal: Trans. Amer. Math. Soc. 357 (2005), 1525-1544
MSC (2000): Primary 34L05
DOI: https://doi.org/10.1090/S0002-9947-04-03553-6
Published electronically: October 5, 2004
MathSciNet review: 2115375
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Abstract: The relation between Hausdorff dimension of the singular spectrum of a Schrödinger operator and the decay of its potential has been extensively studied in many papers. In this work, we address similar questions from a different point of view. Our approach relies on the study of the so-called Krein systems. For Schrödinger operators, we show that some bounds on the singular spectrum, obtained recently by Remling and Christ-Kiselev, are optimal.


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Additional Information

S. Denisov
Affiliation: Department of Mathematics, 253-37, Caltech, Pasadena, California 91125
Email: denissov@its.caltech.edu

S. Kupin
Affiliation: Department of Mathematics, 253-37, Caltech, Pasadena, California 91125
Address at time of publication: CMI, Université de Provence, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France
Email: kupin@its.caltech.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03553-6
Keywords: Schr\"odinger operators, Dirac operators, Krein systems, singular part of the spectral measure
Received by editor(s): February 27, 2002
Received by editor(s) in revised form: November 4, 2003
Published electronically: October 5, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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