Details
| Original language | English |
|---|---|
| Journal | Annales Henri Poincare |
| Early online date | 17 Feb 2025 |
| Publication status | E-pub ahead of print - 17 Feb 2025 |
Abstract
We investigate the negative part of the spectrum of the operator -∂2-μ on L2(R), where a locally finite Radon measure μ≥0 serves as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb–Thirring type. A crucial tool for our estimates is Otelbaev’s function, a certain average of the measure-potential μ, which is used both in the proofs and the formulation of most of the results.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematics(all)
- Mathematical Physics
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In: Annales Henri Poincare, 17.02.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Negative Eigenvalue Estimates for the 1D Schrödinger Operator with Measure-Potential
AU - Fulsche, Robert
AU - Nursultanov, Medet
AU - Rozenblum, Grigori
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025/2/17
Y1 - 2025/2/17
N2 - We investigate the negative part of the spectrum of the operator -∂2-μ on L2(R), where a locally finite Radon measure μ≥0 serves as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb–Thirring type. A crucial tool for our estimates is Otelbaev’s function, a certain average of the measure-potential μ, which is used both in the proofs and the formulation of most of the results.
AB - We investigate the negative part of the spectrum of the operator -∂2-μ on L2(R), where a locally finite Radon measure μ≥0 serves as a potential. We obtain estimates for the eigenvalue counting function, for individual eigenvalues and estimates of the Lieb–Thirring type. A crucial tool for our estimates is Otelbaev’s function, a certain average of the measure-potential μ, which is used both in the proofs and the formulation of most of the results.
UR - http://www.scopus.com/inward/record.url?scp=85218179165&partnerID=8YFLogxK
U2 - 10.1007/s00023-025-01549-z
DO - 10.1007/s00023-025-01549-z
M3 - Article
AN - SCOPUS:85218179165
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
ER -