{"paper":{"title":"Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.SP","authors_text":"Penghui Wang, Xijun Hu","submitted_at":"2015-04-08T03:14:32Z","abstract_excerpt":"Let $\\lambda_j$ be the $j$-th eigenvalue of Sturm-Liouville systems with separated boundary conditions, we build up the Hill-type formula, which represent $\\prod\\limits_{j}(1-\\lambda_j^{-1})$ as a determinant of finite matrix. This is the first attack on such a formula under non-periodic type boundary conditions. Consequently, we get the Krein-type trace formula based on the Hill-type formula, which express $\\sum\\limits_{j}{1\\over \\lambda_j^m}$ as trace of finite matrices. The trace formula can be used to estimate the conjugate point alone a geodesic in Riemannian manifold and to get some infi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01817","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"}