Localization principles for Schrödinger operator with a singular matrix potential

Authors

  • V. A. Mikhailets </span>Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs&rsquo;ka, Kyiv, 01601, Ukraine; https://orcid.org/0000-0002-1332-1562
  • A. A. Murach </span>Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs&rsquo;ka, Kyiv, 01601, Ukraine
  • V. Novikov Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs&rsquo;ka, Kyiv, 01601, Ukraine&nbsp;

DOI:

Keywords:

Schrödinger operator, singular potential, semiboundedness, discrete spectrum, Molchanov’s criterion

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.

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Published

2017-12-25

Issue

Vol. 23 No. 4 (2017)

Section

Articles

How to Cite

Mikhailets, V. A., et al. “Localization Principles for Schrödinger Operator With a Singular Matrix Potential”. Methods of Functional Analysis and Topology, vol. 23, no. 4, Dec. 2017, pp. 367-7, https://zen.imath.kiev.ua/index.php/mfat/article/view/677.