Damanik, David and Killip, Rowan (2004) Half-line Schrödinger operators with no bound states. Acta Mathematica, 193 (1). pp. 31-72. ISSN 0001-5962. doi:10.1007/bf02392550. https://resolver.caltech.edu/CaltechAUTHORS:20191127-104111258
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Abstract
We consider Schödinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if Δ+V has no spectrum outside of the interval [−2,2], then it has purely absolutely continuous spectrum. In the continuum case we show that if both −Δ+V and −Δ−V have no spectrum outside [0,∞), then both operators are purely absolutely continuous. These results extend to operators with finitely many bound states.
Item Type: | Article | |||||||||
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Additional Information: | © 2004 by Institut Mittag-Leffler. Received March 11, 2003; Received in revised form November 14, 2003. The first author was supported in part by NSF grants DMS-0227289 and INT-0204308. | |||||||||
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Issue or Number: | 1 | |||||||||
DOI: | 10.1007/bf02392550 | |||||||||
Record Number: | CaltechAUTHORS:20191127-104111258 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20191127-104111258 | |||||||||
Official Citation: | Damanik, David; Killip, Rowan. Half-line Schrödinger operators with no bound states. Acta Math. 193 (2004), no. 1, 31-72. doi:10.1007/BF02392550. https://projecteuclid.org/euclid.acta/1485891668 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 100099 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Tony Diaz | |||||||||
Deposited On: | 27 Nov 2019 18:49 | |||||||||
Last Modified: | 16 Nov 2021 17:51 |
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