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Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices

Frank, Rupert L. and Simon, Barry (2011) Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices. Duke Mathematical Journal, 157 (3). pp. 461-493. ISSN 0012-7094. https://resolver.caltech.edu/CaltechAUTHORS:20110502-112300651

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Abstract

We prove bounds of the form ∑_(e∈I⋂σ_d(H)) dist(e, σ_e(H)^(1/2) ≤ L^1 -norm of a perturbation, where I is a gap. Included are gaps in continuum one-dimensional periodic Schrödinger operators and finite gap Jacobi matrices, where we get a generalized Nevai conjecture about an L^(1)-condition implying a Szegő condition. One key is a general new form of the Birman-Schwinger bound in gaps.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1215/00127094-1272912DOIArticle
http://projecteuclid.org/euclid.dmj/1301678730PublisherArticle
https://arxiv.org/abs/1003.4703arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 2011 Duke University Press. Received 16 March 2010; Revision received 4 July 2010. Simon’s work supported in part by National Science Foundation grant DMS-0652919. We thank Alexander Pushnitski and Robert Seiringer for valuable discussions.
Funders:
Funding AgencyGrant Number
NSFDMS-0652919
Issue or Number:3
Classification Code:2010 Mathematics Subject Classification: Primary Subjects: 35P15, 35J10, 47B36
Record Number:CaltechAUTHORS:20110502-112300651
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110502-112300651
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:23521
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:03 May 2011 20:14
Last Modified:03 Oct 2019 02:47

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