On the spectral L2 conjecture, 3/2-Lieb-Thirring inequality and distributional potentials

DOI10.1063/1.2142837zbMath1111.81063OpenAlexW2005194991WikidataQ123218829 ScholiaQ123218829MaRDI QIDQ3438720

Alexei Rybkin

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.2142837

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Applications of operator theory in the physical sciences (47N50) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items (4)

Spectral analysis of the half-line Kronig-Penney model with Wigner-von Neumann perturbations ⋮ Sum rules and spectral measures of Schrödinger operators with \(L^2\) potentials ⋮ On the absolutely continuous spectrum of generalized indefinite strings ⋮ On the absolutely continuous spectrum of generalized indefinite strings. II

Cites Work

• Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• On the existence of the absolutely continuous component for the measure associated with some orthogonal systems
• On new relations between spectral properties of Jacobi matrices and their coefficients
• Sum rules for Jacobi matrices and their applications to spectral theory
• Sturm-Liouville operators with singular potentials
• Transformation operators for Sturm--Liouville operators with singular potentials
• On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)
• Schrödinger operators in the twentieth century
• On the absolutely continuous and negative discrete spectra of Schrödinger operators on the line with locally integrable globally square summable potentials
• First KdV integrals and absolutely continuous spectrum for 1-D Schrödinger operator

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