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. https://resolver.caltech.edu/CaltechAUTHORS:DAMpams06
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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 as this energy tends to the bottom of the essential spectrum.
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| 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. | ||||||
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| Subject Keywords: | Discrete Schrödinger operators, bound states, oscillation theory | ||||||
| Issue or Number: | 4 | ||||||
| DOI: | 10.1090/S0002-9939-06-08550-9 | ||||||
| Record Number: | CaltechAUTHORS:DAMpams06 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:DAMpams06 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 12274 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Tony Diaz | ||||||
| Deposited On: | 14 Nov 2008 04:35 | ||||||
| Last Modified: | 08 Nov 2021 22:27 |
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