Universal monotonicity of eigenvalue moments and sharp Lieb-Thirring inequalities

DOI10.4171/JEMS/233zbMath1201.81056arXiv0810.1573MaRDI QIDQ604435

Joachim Stubbe

Publication date: 11 November 2010

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1573

zbMATH Keywords

Schrödinger operatorsspectral gapLieb-Thirring inequalitiesphase space boundsuniversal bounds for eigenvalues

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Spectral Inequalities for Quantum Graphs ⋮ Trace identities for commutators, with applications to the distribution of eigenvalues

Cites Work

• Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
• A simple proof of a theorem of Laptev and Weidl
• Sharp Lieb-Thirring inequalities in high dimensions.
• Universal Bounds and Semiclassical Estimates for Eigenvalues of Abstract Schrödinger Operators
• On trace identities and universal eigenvalue estimates for some partial differential operators
• BOUND STATES FOR SCHRÖDINGER HAMILTONIANS: PHASE SPACE METHODS AND APPLICATIONS
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