Localization principles for Schrödinger operator with a singular matrix potential

Abstract

We study the spectrum of the one-dimensional Schrödinger operator $H_0$ with a matrix singular distributional potential $q=Q^{\prime }$ where $Q\in L_{\mathrm{loc}}^2(\mathbb{R},{\mathbb{C}}^m)$. We obtain generalizations of Ismagilov's localization principles, which give necessary and sufficient conditions for the spectrum of $H_0$ to be bounded below and discrete.

14 pages

Cited by in corpus (1)

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