A Caltech Library Service

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.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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 Paper
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.
Funding AgencyGrant Number
Issue or Number:1
Record Number:CaltechAUTHORS:20191127-104111258
Persistent URL:
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.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100099
Deposited By: Tony Diaz
Deposited On:27 Nov 2019 18:49
Last Modified:16 Nov 2021 17:51

Repository Staff Only: item control page