Published April 15, 2011
| Version Submitted + Published
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Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices
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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.
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.Attached Files
Published - Frank2011p13678Duke_Math_J.pdf
Submitted - 1003.4703
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Frank2011p13678Duke_Math_J.pdf
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Additional details
Identifiers
- Eprint ID
- 23521
- Resolver ID
- CaltechAUTHORS:20110502-112300651
Related works
- Describes
- https://arxiv.org/abs/1003.4703 (URL)
Funding
- NSF
- DMS-0652919
Dates
- Created
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2011-05-03Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field