{"paper":{"title":"Inverse scattering for the 1-D Helmholtz equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ingrid Beltita, Renata Bunoiu","submitted_at":"2005-11-16T07:11:48Z","abstract_excerpt":"We prove a uniqueness result for Nevanlinna functions. and this result is then used to give an elementary proof of the uniqueness in the inverse scattering problem for the equation $ u\" + \\frac{k^2}{c^2}u=0 $ on $\\mathbb R$. Here $c$ is a real positive measurable function that is bounded from below by a positive constant, and is close to $1$ at $\\pm \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511401","kind":"arxiv","version":5},"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"}