English

No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators

Spectral Theory 2023-01-18 v1

Abstract

It is known that the spectrum of Schr\"odinger operators with sparse potentials consists of singular continuous spectrum. We give a sufficient condition so that the edge of the singular continuous spectrum is not an eigenvalue and construct examples with singular continuous spectrum which have no eigenvalues and which have a single negative eigenvalue.

Keywords

Cite

@article{arxiv.2301.05899,
  title  = {No eigenvectors embedded in the singular continuous spectrum of Schr\"odinger operators},
  author = {Kota Ujino},
  journal= {arXiv preprint arXiv:2301.05899},
  year   = {2023}
}