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Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices

Hundertmark, Dirk and Simon, Barry (2008) Eigenvalue bounds in the gaps of Schrödinger operators and Jacobi matrices. Journal of Mathematical Analysis and Applictions, 340 (2). pp. 892-900. ISSN 0022-247X. doi:10.1016/j.jmaa.2007.08.059.

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We consider C = A + B where A is selfadjoint with a gap (a, b) in its spectrum and B is (relatively) compact. We prove a general result allowing B of indefinite sign and apply it to obtain a (δV)^(d/2) bound for perturbations of suitable periodic Schrödinger operators and a (not quite) Lieb–Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices.

Item Type:Article
Related URLs:
URLURL TypeDescription DOIArticle Paper
Hundertmark, Dirk0000-0002-0643-0138
Simon, Barry0000-0003-2561-8539
Additional Information:© 2007 Elsevier. Received 19 May 2007. Available online 22 September 2007. Submitted by Goong Chen.
Subject Keywords:Eigenvalue bounds; Jacobi matrices; Schrödinger operators
Issue or Number:2
Classification Code:Mathematics Subject Classification. 47B36, 81Q10, 35P15
Record Number:CaltechAUTHORS:20091014-110720129
Persistent URL:
Official Citation:Dirk Hundertmark, Barry Simon, Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices, Journal of Mathematical Analysis and Applications, Volume 340, Issue 2, 15 April 2008, Pages 892-900, ISSN 0022-247X, DOI: 10.1016/j.jmaa.2007.08.059.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16346
Deposited By: Joy Painter
Deposited On:26 Oct 2009 19:04
Last Modified:08 Nov 2021 23:26

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