English

Non-accretive Schr\"odinger operators and exponential decay of their eigenfunctions

Spectral Theory 2018-11-26 v1 Mathematical Physics Analysis of PDEs math.MP

Abstract

We consider non-self-adjoint electromagnetic Schr\"odinger operators on arbitrary open sets with complex scalar potentials whose real part is not necessarily bounded from below. Under a suitable sufficient condition on the electromagnetic potential, we introduce a Dirichlet realisation as a closed densely defined operator with non-empty resolvent set and show that the eigenfunctions corresponding to discrete eigenvalues satisfy an Agmon-type exponential decay.

Keywords

Cite

@article{arxiv.1605.02437,
  title  = {Non-accretive Schr\"odinger operators and exponential decay of their eigenfunctions},
  author = {David Krejcirik and Nicolas Raymond and Julien Royer and Petr Siegl},
  journal= {arXiv preprint arXiv:1605.02437},
  year   = {2018}
}