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.
Full Text
Article Information
| Title | Schrödinger operators with measure-valued potentials:
semiboundedness and spectrum |
| Source | Methods Funct. Anal. Topology, Vol. 24 (2018), no. 3, 240-254 |
| MathSciNet |
MR3860804 |
| Milestones | Received 25/06/2018 |
| Copyright | The 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
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},
MRNUMBER = {MR3860804},
URL = {http://mfat.imath.kiev.ua/article/?id=1084},
}
