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.
Full Text
Article Information
| Title | Localization principles for Schrödinger operator with a singular matrix potential |
| Source | Methods Funct. Anal. Topology, Vol. 23 (2017), no. 4, 367-377 |
| MathSciNet |
MR3745187 |
| Milestones | Received 10/08/2017 |
| Copyright | The 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
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},
MRNUMBER = {MR3745187},
URL = {http://mfat.imath.kiev.ua/article/?id=1004},
}
