Principles of localization for one-dimensional Schrödinger operator with distribution potential

Abstract

In the paper, we investigate the spectrum of Shrodinger' operator $L$ with distribution potential from the space $H^{-1}_{loc}(\mathbb{R},\mathbb{R})$. We obtain a generalization of Ismagilov's principles of localizations which gives necessary and sufficient conditions for the spectrum of the operator $L$ to be bounded from below and discrete.