Open problems: Lieb-Thirring type inequalities for Schrödinger operators with a complex-valued potential

DOI10.1007/S00020-012-2021-5zbMath1279.47071OpenAlexW1996368962MaRDI QIDQ1946578

Marcel Hansmann, Guy Katriel, Michael Demuth

Publication date: 15 April 2013

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-012-2021-5

zbMATH Keywords

Schrödinger operatorLieb-Thirring inequalitycomplex valued potential

Mathematics Subject Classification ID

Problem books (00A07) Spectral theory and eigenvalue problems for partial differential equations (35P99) General theory of partial differential operators (47F05) Schrödinger operator, Schrödinger equation (35J10)

Related Items (13)

Spectral enclosures for Dirac operators perturbed by rigid potentials ⋮ Schrödinger operators with complex sparse potentials ⋮ Bounds on eigenvalues of perturbed Lamé operators with complex potentials ⋮ \(L_p\)-spectrum and Lieb-Thirring inequalities for Schrödinger operators on the hyperbolic plane ⋮ Trace formulas for a complex KdV equation ⋮ Number of eigenvalues of non-self-adjoint Schrödinger operators with dilation analytic complex potentials ⋮ On non-round points of the boundary of the numerical range and an application to non-selfadjoint Schrödinger operators ⋮ Eigenvalue bounds for non-self-adjoint Schrödinger operators with nontrapping metrics ⋮ On compressed resolvents of Schrödinger operators with complex potentials ⋮ On quantitative bounds on eigenvalues of a complex perturbation of a Dirac operator ⋮ Schrödinger operator with non-zero accumulation points of complex eigenvalues ⋮ Eigenvalue bounds and spectral stability of Lamé operators with complex potentials ⋮ On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators

Cites Work

• 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 estimates for Schrödinger operators with complex potentials
• Bounds on complex eigenvalues and resonances
• Eigenvalues of Non-selfadjoint Operators: A Comparison of Two Approaches
• Eigenvalue bounds for Schrödinger operators with complex potentials
• Lieb–Thirring estimates for non-self-adjoint Schrödinger operators
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