{"paper":{"title":"Half-line Schrodinger Operators With No Bound States","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"David Damanik, Rowan Killip","submitted_at":"2003-02-28T22:52:21Z","abstract_excerpt":"We consider Sch\\\"odinger operators on the half-line, both discrete and continuous, and show that the absence of bound states implies the absence of embedded singular spectrum. More precisely, in the discrete case we prove that if $\\Delta + V$ has no spectrum outside of the interval $[-2,2]$, then it has purely absolutely continuous spectrum. In the continuum case we show that if both $-\\Delta + V$ and $-\\Delta - V$ have no spectrum outside $[0,\\infty)$, then both operators are purely absolutely continuous. These results extend to operators with finitely many bound states."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0303001","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"}