Published April 2010
| Version Published + Submitted
Journal Article
Open
Equality of the Spectral and Dynamical Definitions of Reflection
Abstract
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.
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.Attached Files
Published - Breuer2010p7191Commun_Math_Phys.pdf
Submitted - 0905.3724
Files
Breuer2010p7191Commun_Math_Phys.pdf
Additional details
Identifiers
- Eprint ID
- 17610
- Resolver ID
- CaltechAUTHORS:20100301-083137497
Related works
- Describes
- https://arxiv.org/abs/0905.3724 (URL)
Funding
- NSF
- DMS-0652919
Dates
- Created
-
2010-03-10Created from EPrint's datestamp field
- Updated
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2021-11-08Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department , Physics Department