Spectral gaps of Schr\"odinger operators with periodic singular potentials

Plamen Djakov; Boris Mityagin

Spectral gaps of Schr\"odinger operators with periodic singular potentials

Spectral Theory 2009-03-31 v1

Authors: Plamen Djakov , Boris Mityagin

Abstract

By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schr\"odinger operators with periodic singular potentials $v.$ Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption $v \in H^{-1}_{loc} (\mathbb{R}).$ They extend and strengthen similar results proved in the classical case $v \in L^2_{loc}(\mathbb{R}).$

Keywords

Schrödinger operators periodic singular potentials spectral gaps Fourier method quasi-derivatives smoothness of potentials

Cite

@article{arxiv.0903.5210,
  title  = {Spectral gaps of Schr\"odinger operators with periodic singular potentials},
  author = {Plamen Djakov and Boris Mityagin},
  journal= {arXiv preprint arXiv:0903.5210},
  year   = {2009}
}

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