{"paper":{"title":"Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Lukas Schimmer","submitted_at":"2013-10-14T18:05:32Z","abstract_excerpt":"In this paper we approximate a Schr\\\"odinger operator on $L^2(\\R)$ by Jacobi operators on $\\ell^2(\\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\\gamma=1/2$ and $\\gamma=3/2$. To this end we first investigate spectral inequalities for Jacobi operators. Using the commutation method we present a new, direct proof of a sharp inequality corresponding to a Lieb-Thirring inequality for the power 3/2 on $\\ell^2(\\Z)$. We also introduce inequalities for higher powers of the eigenvalues as well as for matrix-valued potentials and compare our results to previously establish"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3764","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}