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15 April 2011 Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices
Rupert L. Frank, Barry Simon
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Duke Math. J. 157(3): 461-493 (15 April 2011). DOI: 10.1215/00127094-1272912

Abstract

We prove bounds of the form eIσd(H)dist(e,σe(H))1/2L1-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 L1-condition implying a Szegő condition. One key is a general new form of the Birman-Schwinger bound in gaps.

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Rupert L. Frank. Barry Simon. "Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices." Duke Math. J. 157 (3) 461 - 493, 15 April 2011. https://doi.org/10.1215/00127094-1272912

Information

Published: 15 April 2011
First available in Project Euclid: 1 April 2011

zbMATH: 1229.35157
MathSciNet: MR2785827
Digital Object Identifier: 10.1215/00127094-1272912

Subjects:
Primary: 35J10 , 35P15 , 47B36

Rights: Copyright © 2011 Duke University Press

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Vol.157 • No. 3 • 15 April 2011
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