02-68 S. Denisov, S. Kupin.
On the singular spectrum of Schrodinger operators with decaying potentials. (43K, LATEX) Feb 14, 02
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Abstract. The relation between Hausdorff dimension of the singular spectrum of a Schrodinger operator and the decay of its potential has been extensively studied. 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 Schrodinger operators, we show that some bounds on the singular spectrum, obtained recently by Remling, are optimal in L^p (R^+) scale.

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