Absolutely continuous and pure point spectra of discrete operators with sparse potentials

@inproceedings{Molchanov2021AbsolutelyCA,
  title={Absolutely continuous and pure point spectra of discrete operators with sparse potentials},
  author={Stanislav Molchanov and Oleg Safronov and Boris Vainberg},
  year={2021}
}
We consider the discrete Schr\”odinger operator $H=-\Delta+V$ with a sparse potential $V$ and find conditions guaranteeing either existence of wave operators for the pair $H$ and $H_0=-\Delta$, or presence of dense purely point spectrum of the operator $H$ on some interval $[\lambda_0,0]$ with $\lambda_0<0$. 

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