Dirk Hundertmark and Barry Simon
Eigenvalue bounds in the gaps of Schrodinger operators and Jacobi matrices
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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.