{"paper":{"title":"Optimal bounds on the fundamental spectral gap with single-well potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Evans M. Harrell II, Zakaria El Allali","submitted_at":"2018-07-22T17:46:53Z","abstract_excerpt":"We characterize the potential-energy functions $V(x)$ that minimize the gap $\\Gamma$ between the two lowest Sturm-Liouville eigenvalues for \\[ H(p,V) u := -\\frac{d}{dx} \\left(p(x)\\frac{du}{dx}\\right)+V(x) u = \\lambda u, \\quad\\quad x\\in [0,\\pi ], \\] where separated self-adjoint boundary conditions are imposed at end points, and $V$ is subject to various assumptions, especially convexity or having a \"single-well\" form. In the classic case where $p=1$ we recover with different arguments the result of Lavine that $\\Gamma$ is uniquely minimized among convex $V$ by the constant, and in the case of s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08328","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"}