Schrödinger operators with measure-valued potentials: semiboundedness and spectrum

Abstract

We study the 1-D Schrödinger operators in Hilbert space $L^2(\mathbb{R})$ with real-valued Radon measure $q^{\prime }(x)$, $q\in {\mathrm{BV}}_{loc}(\mathbb{R})$ as potentials. New sufficient conditions for minimal operators to be bounded below and selfadjoint are found. For such operators a criterion for the discreteness of the spectrum is proved, which generalizes Molchanov's, Brinck's, and the Albeverio-Kostenko-Malamud criteria. The quadratic forms corresponding to the investigated operators are described.

arXiv comment17 pages

References in corpus (3)

• Remarks on Schrödinger operators with singular matrix potentials
• Schrödinger operators with complex singular potentials
• Localization principles for Schrödinger operator with a singular matrix potential

Cited by in corpus (1)

• Spectral Theory for Sturm-Liouville operators with measure potentials through Otelbaev's function