On the Consistency of Compressed Modes for Variational Problems Associated with the Schrödinger Operator

@article{Barekat2014OnTC,
  title={On the Consistency of Compressed Modes for Variational Problems Associated with the Schr{\"o}dinger Operator},
  author={Farzin Barekat},
  journal={SIAM J. Math. Analysis},
  year={2014},
  volume={46},
  pages={3568-3577}
}
This paper provides theoretical consistency results for compressed modes. We prove that as L1 regularization term in certain non-convex variational optimization problems vanishes, the solutions of the optimization problem and the corresponding eigenvalues converge to Wannier-like functions and the eigenvalues of the Hamiltonian, respectively. 

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