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A version of Gordon's theorem for multi-dimensional Schrödinger operators

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.

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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.

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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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MathSciNet review2022708
Classification Code:MSC (2000): Primary 81Q10, 47B39
Record Number: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
Deposited By: Tony Diaz
Deposited On:30 Aug 2011 21:06
Last Modified:26 Dec 2012 13:38

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