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Equality of the Spectral and Dynamical Definitions of Reflection

Breuer, Jonathan and Ryckman, Eric and Simon, Barry (2010) Equality of the Spectral and Dynamical Definitions of Reflection. Communications in Mathematical Physics, 295 (2). pp. 531-550. ISSN 0010-3616.

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For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = −∞ as t → −∞ goes entirely to x = ∞ as t → ∞. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 2009 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 12 May 2009. Accepted: 10 August 2009. Published online: 14 November 2009. Communicated by M. Aizenman. Supported in part by NSF grant DMS-0652919.
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Issue or Number:2
Record Number:CaltechAUTHORS:20100301-083137497
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Official Citation:Breuer, J., Ryckman, E. & Simon, B. Commun. Math. Phys. (2010) 295: 531. doi:10.1007/s00220-009-0945-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:17610
Deposited By: Tony Diaz
Deposited On:10 Mar 2010 17:55
Last Modified:03 Oct 2019 01:30

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