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Half-line Schrödinger operators with no bound states

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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/bf02392550DOIArticle
https://arxiv.org/abs/math-ph/0303001arXivDiscussion Paper
ORCID:
AuthorORCID
Damanik, David0000-0001-5924-3849
Killip, Rowan0000-0002-4272-7916
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0227289
NSFINT-0204308
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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