Spectral gaps of Schrödinger operators with periodic singular potentials

Details Spectral gaps of Schrödinger operators with periodic singular potentials Spectral gaps of Schrödinger operators with periodic singular potentials

2009-03-30

arxiv.org/abs/0903.5210v1

Mathematics

Spectral Theory

Scientific paper

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 $v \in L^2_{loc}(\mathbb{R}).$

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