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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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

Authors: David Damanik and Gerald Teschl
Journal: Proc. Amer. Math. Soc. 135 (2007), 1123-1127
MSC (2000): Primary 47B36, 81Q10; Secondary 39A11, 47B39
Published electronically: October 4, 2006
MathSciNet review: 2262914
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Abstract: 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 $ E$ as this energy tends to the bottom of the essential spectrum.

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Additional Information

David Damanik
Affiliation: Mathematics 253–37, California Institute of Technology, Pasadena, California 91125

Gerald Teschl
Affiliation: Faculty of Mathematics, Nordbergstrasse 15, 1090 Wien, Austria – and – International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria

PII: S 0002-9939(06)08550-9
Keywords: Discrete Schr\"odinger operators, bound states, oscillation theory
Received by editor(s): September 3, 2005
Received by editor(s) in revised form: November 9, 2005
Published electronically: October 4, 2006
Additional Notes: This work was supported by the National Science Foundation under Grant No.\ DMS-0500910 and the Austrian Science Fund (FWF) under Grant No.\ P17762
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society