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
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.
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
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},
}
