具有周期奇异势的薛定谔算子的谱隙
Spectral gaps of Schrödinger operators with periodic singular potentials
摘要：
本文利用拟导数方法研究了具有周期奇异势$v.$的一维Schr dinger算子的谱隙。我们的结果揭示了在先验假设$v \in H^{-1}_{loc} (\mathbb{R}).$下势的光滑性与谱隙渐近性之间的密切关系。它们推广和加强了经典情形$v \in L^2_{loc}(\mathbb{R}).$中的类似结果。
英文摘要：
By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger 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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