On the singular spectrum of Schrödinger operators with decaying potential

Denisov, S.; Kupin, S.

doi:10.1090/S0002-9947-04-03553-6

On the singular spectrum of Schrödinger operators with decaying potential
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by S. Denisov and S. Kupin PDF

Trans. Amer. Math. Soc. 357 (2005), 1525-1544 Request permission

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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