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arXiv · 1810.06363

Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum

Vladimir Mikhailets·Volodymyr Molyboga
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Abstract

We study the 1-D Schr\"odinger operators in Hilbert space $L^{2}(\mathbb{R})$ with real-valued Radon measure $q'(x)$, $q\in \mathrm{BV}_{loc}(\mathbb{R})$ 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.

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Vladimir Mikhailets, Volodymyr Molyboga. 2018-10-15. Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum. https://arxiv.org/abs/1810.06363

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