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Schrödinger operators with measure-valued potentials: semiboundedness and spectrum


Abstract

We study 1-D Schrödinger operators in the Hilbert space $L^{2}(\mathbb{R})$ a 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 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.

Key words: Schrödinger operators, strongly singular potentials, discrete spectrum, Molchanov's criterion.


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Article Information

TitleSchrödinger operators with measure-valued potentials: semiboundedness and spectrum
SourceMethods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 240-254
MilestonesReceived 25/06/2018
CopyrightThe Author(s) 2018 (CC BY-SA)

Authors Information

V. Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine

V. Molyboga
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka str., Kyiv, 01601, Ukraine


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Citation Example

Vladimir Mikhailets and Volodymyr Molyboga, Schrödinger operators with measure-valued potentials: semiboundedness and spectrum, Methods Funct. Anal. Topology 24 (2018), no. 3, 240-254.


BibTex

@article {MFAT1084,
    AUTHOR = {Vladimir Mikhailets and Volodymyr Molyboga},
     TITLE = {Schrödinger operators with measure-valued potentials:
semiboundedness and spectrum},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {24},
      YEAR = {2018},
    NUMBER = {3},
     PAGES = {240-254},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1084},
}


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