loading page

Absolutely continuous and pure point spectra of discrete operators with sparse potentials
  • S. Molchanov,
  • O. Safronov,
  • B. Vainberg
S. Molchanov
UNC Charlotte

Corresponding Author:[email protected]

Author Profile
O. Safronov
UNC Charlotte
Author Profile
B. Vainberg
UNC Charlotte
Author Profile


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 $\lambda_0<0$.
09 Dec 2021Submitted to Mathematical Methods in the Applied Sciences
16 Dec 2021Submission Checks Completed
16 Dec 2021Assigned to Editor
17 Dec 2021Reviewer(s) Assigned
09 May 2022Review(s) Completed, Editorial Evaluation Pending
11 May 2022Editorial Decision: Accept
Jun 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8435