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Bound states of discrete Schrödinger operators with super-critical inverse square potentials

Damanik, David and Teschl, Gerald (2007) Bound states of discrete Schrödinger operators with super-critical inverse square potentials. Proceedings of the American Mathematical Society, 135 (4). pp. 1123-1127. ISSN 0002-9939. doi:10.1090/S0002-9939-06-08550-9.

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We consider discrete one-dimensional Schrödinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of the number of eigenvalues below a given energy as this energy tends to the bottom of the essential spectrum.

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Damanik, David0000-0001-5924-3849
Additional Information:©2006 American Mathematical Society. Communicated by Joseph A. Ball. Received by the editors September 3, 2005 and, in revised form, November 9, 2005. Article electronically published on October 4, 2006. Gerald Teschl gratefully acknowledges the extraordinary hospitality of the Department of Mathematics at Caltech, where this work was done. This work was supported by the National Science Foundation under Grant No. DMS-0500910 and the Austrian Science Fund (FWF) under Grant No. P17762.
Funding AgencyGrant Number
National Science FoundationDMS-0500910
Austrian Science Fund (FWF)P17762
Subject Keywords:Discrete Schrödinger operators, bound states, oscillation theory
Issue or Number:4
Record Number:CaltechAUTHORS:DAMpams06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12274
Deposited By: Tony Diaz
Deposited On:14 Nov 2008 04:35
Last Modified:08 Nov 2021 22:27

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