{"paper":{"title":"On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2","license":"","headline":"","cross_cats":["funct-an","math.FA"],"primary_cat":"quant-ph","authors_text":"Timo Weidl","submitted_at":"1995-04-17T12:29:16Z","abstract_excerpt":"Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\\\"odinger operator $Hu:=-u^{\\prime\\prime}-Vu,\\ V\\geq 0,$ on $L_2({\\Bbb R})$.  We prove the inequality \\sum_i|E_i(H)|^\\gamma\\leq L_{\\gamma,1}\\int_{\\Bbb R} V^{\\gamma+1/2}(x)dx, (1) for the \"limit\" case $\\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\\gamma,1}$ in (1), as $1/2<\\gamma<3/2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9504013","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"}