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

Vladimir Mikhailets; Volodymyr Molyboga

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

Spectral Theory 2018-10-16 v1

Authors: Vladimir Mikhailets , Volodymyr Molyboga

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.

Keywords

schrödinger operators magnetic schrödinger operator operator theory on hilbert spaces

Cite

@article{arxiv.1810.06363,
  title  = {Schr\"odinger operators with measure-valued potentials: semiboundedness and spectrum},
  author = {Vladimir Mikhailets and Volodymyr Molyboga},
  journal= {arXiv preprint arXiv:1810.06363},
  year   = {2018}
}

Comments

17 pages

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