Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices

Abstract

We prove bounds of the form $\sum_{e\in I\capσ_\di (H)} \dist (e,σ_\e (H))^{1/2} \leq L^1$-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.

Corrected typos and added reference

References in corpus (5)

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Cited by in corpus (6)

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• Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices
• Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices