Damanik, David (2004) A version of Gordon's theorem for multi-dimensional Schrödinger operators. Transactions of the American Mathematical Society, 356 (2). pp. 495-507. ISSN 0002-9947 http://resolver.caltech.edu/CaltechAUTHORS:20110829-153829965
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Abstract
We consider discrete Schrödinger operators in H = Δ + V in ℓ^2(Z^d) with d ≥ 1, and study the eigenvalue problem for these operators. It is shown that the point spectrum is empty if the potential V is sufficiently well approximated by periodic potentials. This criterion is applied to quasiperiodic V and to so-called Fibonacci-type superlattices.
| Item Type: | Article | ||||
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| Additional Information: | © 2003 American Mathematical Society. Received by the editors October 9, 2001. Article electronically published on September 22, 2003. This research was partially supported by NSF grant DMS-0010101. | ||||
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| Classification Code: | MSC (2000): Primary 81Q10, 47B39 | ||||
| Record Number: | CaltechAUTHORS:20110829-153829965 | ||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20110829-153829965 | ||||
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| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||
| ID Code: | 25154 | ||||
| Collection: | CaltechAUTHORS | ||||
| Deposited By: | Tony Diaz | ||||
| Deposited On: | 30 Aug 2011 21:06 | ||||
| Last Modified: | 26 Dec 2012 13:38 |
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