Remarks on eigenvalue estimates and semigroup domination

2009/03/03 by Rupert L. Frank, Frank, Rupert L.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Spectral Theory (math.SP) #math-ph #math.MP #math.SP

paper · pdf · doi:10.48550/arxiv.0903.0561

26 pages

arxiv created 2009/03/03 · openalex publication_date 2009/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an overview over recent results concerning semi-classical spectral estimates for magnetic Schroedinger operators. We discuss how the constants in magnetic and non-magnetic eigenvalue bounds are related and we prove, in an abstract setting, that any non-magnetic Lieb-Thirring-type inequality implies a magnetic Lieb-Thirring-type inequality with possibly a larger constant.

Related

• Eigenvalue estimates for magnetic Schroedinger operators in domains
• Lieb-Thirring type inequalities for non self-adjoint perturbations of magnetic Schrödinger operators
• Eigenvalue asymptotics for confining magnetic Schrödinger operators with complex potentials
• Spectral Asymptotics for Magnetic Schroedinger Operator
• Semiclassical analysis of Schrödinger operators with magnetic wells