Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices

Details Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices

2007-05-24

arxiv.org/abs/0705.3646v1

Mathematics

Spectral Theory

Scientific paper

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.

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