{"paper":{"title":"Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schr\\\"odinger Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Barry Simon, Fritz Gesztesy","submitted_at":"2003-07-01T12:02:08Z","abstract_excerpt":"Let V_0 be a real-valued function on [0,\\infty) and V\\in L^1([0,R]) for all R>0 so that H(V_0)= -\\f{d^2}{dx^2}+V_0 in L^2([0,\\infty)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let \\calM (V_0) be the set of V so that H(V) and H(V_0) have the same spectrum. We prove that \\calM(V_0) is connected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307007","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"}