Pseudospectra of the Schroedinger operator with a discontinuous complex potential

@article{Henry2015PseudospectraOT,
  title={Pseudospectra of the Schroedinger operator with a discontinuous complex potential},
  author={Raphael Henry and David Krej{\vc}iř{\'i}k},
  journal={arXiv: Spectral Theory},
  year={2015}
}
We study spectral properties of the Schroedinger operator with an imaginary sign potential on the real line. By constructing the resolvent kernel, we show that the pseudospectra of this operator are highly non-trivial, because of a blow-up of the resolvent at infinity. Furthermore, we derive estimates on the location of eigenvalues of the operator perturbed by complex potentials. The overall analysis demonstrates striking differences with respect to the weak-coupling behaviour of the Laplacian. 

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