Transactions of the American Mathematical Society

Author(s): S. Denisov; S. Kupin
Journal: Trans. Amer. Math. Soc. 357 (2005), 1525-1544.
MSC (2000): Primary 34L05
Posted: October 5, 2004
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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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S. Denisov
Affiliation: Department of Mathematics, 253-37, Caltech, Pasadena, California 91125
Email: denissov@its.caltech.edu

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