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.
Original language | American English |
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Pages (from-to) | 531-550 |
Number of pages | 20 |
Journal | Communications in Mathematical Physics |
Volume | 295 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2010 |
Externally published | Yes |
Bibliographical note
Funding Information:Supported in part by NSF grant DMS-0652919.