Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices

Abstract

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 $(\delta V{)}^{d/2}$ bound for perturbations of suitable periodic Schrodinger operators and a (not quite)Lieb-Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices.

References in corpus (2)

• Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
• Critical Lieb-Thirring bounds for one-dimensional Schrodinger operators and Jacobi matrices with regular ground states

Cited by in corpus (10)

• Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States
• Operator theoretic methods for the eigenvalue counting function in spectral gaps
• Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps
• Critical Lieb-Thirring Bounds in Gaps and the Generalized Nevai Conjecture for Finite Gap Jacobi Matrices
• Finite Gap Jacobi Matrices: An Announcement
• Twelve Tales in Mathematical Physics: An Expanded Heinemann Prize Lecture
• Finite Gap Jacobi Matrices: A Review
• Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices
• Lieb-Thirring Inequalities for Finite and Infinite Gap Jacobi Matrices
• Finite Gap Jacobi Matrices, I. The Isospectral Torus