Variational Estimates for Discrete Schrödinger Operators with Potentials of Indefinite Sign

@article{Damanik2003VariationalEF,
  title={Variational Estimates for Discrete Schr{\"o}dinger Operators with Potentials of Indefinite Sign},
  author={David Damanik and Dirk Hundertmark and Rowan Killip and Barry Simon},
  journal={Communications in Mathematical Physics},
  year={2003},
  volume={238},
  pages={545-562}
}
AbstractLet H be a one-dimensional discrete Schrödinger operator. We prove that if Σess(H)⊂[−2,2], then H−H0 is compact and Σess(H)=[−2,2]. We also prove that if ${{H_0 + \frac 14 V^2}}$ has at least one bound state, then the same is true for H0+V. Further, if ${{H_0 + \frac 14 V^2}}$ has infinitely many bound states, then so does H0+V. Consequences include the fact that for decaying potential V with ${{\liminf_{{|n|\to\infty}} |nV(n)| > 1}}$, H0+V has infinitely many bound states; the signs of… 

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