{"paper":{"title":"Spectral gap lower bound for the one-dimensional fractional Schr\\\"odinger operator in the interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"Kamil Kaleta","submitted_at":"2011-04-18T14:54:40Z","abstract_excerpt":"We prove the uniform lower bound for the difference $\\lambda_2 - \\lambda_1$ between first two eigenvalues of the fractional Schr\\\"odinger operator, which is related to the Feynman-Kac semigroup of the symmetric $\\alpha$-stable process killed upon leaving open interval $(a,b) \\in \\R $ with symmetric differentiable single-well potential $V$ in the interval $(a,b)$, $\\alpha \\in (1,2)$. \"Uniform\" means that the positive constant appearing in our estimate $\\lambda_2 - \\lambda_1 \\geq C_{\\alpha} (b-a)^{-\\alpha}$ is independent of the potential $V$. In general case of $\\alpha \\in (0,2)$, we also find "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3502","kind":"arxiv","version":2},"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"}