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On the singular spectrum of Schrödinger operators with decaying potential

Denisov, S. and Kupin, S. (2005) On the singular spectrum of Schrödinger operators with decaying potential. Transactions of the American Mathematical Society, 357 (4). pp. 1525-1544. ISSN 0002-9947. doi:10.1090/S0002-9947-04-03553-6.

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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:© Copyright 2004, American Mathematical Society. Received by the editors February 27, 2002 and, in revised form, November 4, 2003. Article electronically published on October 5, 2004. The authors are grateful to B. Simon for valuable discussions on the subject of the article.
Subject Keywords:Schrödinger operators; Dirac operators; Krein systems; singular part of the spectral measure
Issue or Number:4
Classification Code:MSC (2000): Primary 34L05
Record Number:CaltechAUTHORS:20090918-091322613
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15949
Deposited By: George Porter
Deposited On:05 Oct 2009 18:05
Last Modified:08 Nov 2021 23:23

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