On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators

DOI10.4171/JST/378MaRDI QIDQ2078218

Sabine Bögli, František Štampach

Publication date: 28 February 2022

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09794

zbMATH Keywords

Schrödinger operatorJacobi matrixLieb-Thirring inequality

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (7)

Bounds for Schrödinger operators on the half-line perturbed by dissipative barriers ⋮ Volterra-type discrete integral equations and spectra of non-self-adjoint Jacobi operators ⋮ The Lieb–Thirring inequalities: Recent results and open problems ⋮ Schrödinger operators with complex sparse potentials ⋮ The abstract Birman-Schwinger principle and spectral stability ⋮ Lieb-Thirring and Jensen sums for non-self-adjoint Schrödinger operators on the half-line ⋮ Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators

Cites Work

• Schrödinger operator with non-zero accumulation points of complex eigenvalues
• Inequalities for the eigenvalues of non-selfadjoint Jacobi operators
• An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators
• On the discrete spectrum of non-selfadjoint operators
• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states
• A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
• Spectral properties of Kac-Murdock-Szegö matrices with a complex parameter
• Lieb-Thirring inequalities for Jacobi matrices
• On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)
• Open problems: Lieb-Thirring type inequalities for Schrödinger operators with a complex-valued potential
• Lieb-Thirring inequalities for complex finite gap Jacobi matrices
• Lieb--Thirring bounds for complex Jacobi matrices
• A Blaschke-type condition and its application to complex Jacobi matrices
• Eigenvalue bounds for Schrödinger operators with complex potentials. III

This page was built for publication: On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators