New constants in discrete Lieb-Thirring inequalities for Jacobi matrices

DOI10.1007/s10958-010-9869-1zbMath1304.39021arXiv1312.1907OpenAlexW1965436188MaRDI QIDQ467539

J. Herrera, Sumit K. Garg

Publication date: 3 November 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.1907

zbMATH Keywords

Jacobi matricesdiscrete Schrödinger operatorsLieb-Thirring inequalitiesmoments of eigenvalues

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Discrete version of topics in analysis (39A12) Difference operators (39A70)

Related Items (6)

The Lieb–Thirring inequalities: Recent results and open problems ⋮ Sharp interpolation inequalities for discrete operators ⋮ Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuum ⋮ Spectral bounds for polydiagonal Jacobi matrix operators ⋮ Sharp interpolation inequalities for discrete operators and applications ⋮ The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent

Cites Work

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• Lieb-Thirring inequalities with improved constants
• A simple proof of the generalized Lieb-Thirring inequalities in one-space dimension
• A sharp bound for an eigenvalue moment of the one-dimensional Schrödinger operator
• New bounds on the Lieb-Thirring constants
• Sharp Lieb-Thirring inequalities in high dimensions.
• Lieb-Thirring inequalities for Jacobi matrices
• On the Lieb-Thirring constants \(L_{\gamma, 1}\) for \(\gamma \geq 1/2\)

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