Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 012101 |
| Seitenumfang | 23 |
| Fachzeitschrift | Journal of mathematical physics |
| Jahrgang | 63 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 3 Jan. 2022 |
| Publikationsstatus | Veröffentlicht - Jan. 2022 |
Abstract
We investigate the spectral properties of Sturm–Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness of the spectrum and a criterion for the membership of the resolvents to Schatten classes. We give two side estimates for the lower bound of the essential spectrum. Our main tool in achieving this is Otelbaev’s function.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Mathematik (insg.)
- Mathematische Physik
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in: Journal of mathematical physics, Jahrgang 63, Nr. 1, 012101, 01.2022.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Spectral theory for Sturm–Liouville operators with measure potentials through Otelbaev’s function
AU - Fulsche, Robert
AU - Nursultanov, Medet
N1 - Funding Information: M.N. was partially supported by the grant of the Science Committee of Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP13067584). M.N. was partially supported by Grant Nos. ARC DP190103302 and ARC DP190103451 during this work. The authors would like to thank the anonymous referee for the suggestions
PY - 2022/1
Y1 - 2022/1
N2 - We investigate the spectral properties of Sturm–Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness of the spectrum and a criterion for the membership of the resolvents to Schatten classes. We give two side estimates for the lower bound of the essential spectrum. Our main tool in achieving this is Otelbaev’s function.
AB - We investigate the spectral properties of Sturm–Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness of the spectrum and a criterion for the membership of the resolvents to Schatten classes. We give two side estimates for the lower bound of the essential spectrum. Our main tool in achieving this is Otelbaev’s function.
U2 - 10.1063/5.0062669
DO - 10.1063/5.0062669
M3 - Article
AN - SCOPUS:85122999887
VL - 63
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 1
M1 - 012101
ER -