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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 $q=Q'$ where $Q\in L^{2}_{\mathrm{loc}}(\mathbb{R},\mathbb{C}^{m})$. 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.

Key words: Schrödinger operator, singular potential, semiboundedness, discrete spectrum, Molchanov’s criterion.


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Article Information

TitleLocalization principles for Schrödinger operator with a singular matrix potential
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 367-377
MilestonesReceived 10/08/2017
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

Vladimir Mikhailets
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine;
National Technical University of Ukraine ”Igor Sikorsky Kyiv Polytechnic Institute”, 37 Prospect Peremohy, Kyiv, 03056, Ukraine

Aleksandr Murach
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

Viktor Novikov
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine 


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Citation Example

Vladimir Mikhailets, Aleksandr Murach, and Viktor Novikov, Localization principles for Schrödinger operator with a singular matrix potential, Methods Funct. Anal. Topology 23 (2017), no. 4, 367-377.


BibTex

@article {MFAT1004,
    AUTHOR = {Vladimir Mikhailets and Aleksandr Murach and Viktor Novikov},
     TITLE = {Localization principles for Schrödinger operator with a singular matrix potential},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {4},
     PAGES = {367-377},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1004},
}


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