{"paper":{"title":"Local inverse scattering at a fixed energy for radial Schr{\\\"o}dinger operators and localization of the Regge poles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francois Nicoleau (LMJL), Thierry Daud\\'e","submitted_at":"2015-02-08T17:31:33Z","abstract_excerpt":"We study inverse scattering problems at a fixed energy for radial Schr\\\"{o}dinger operators on $\\R^n$, $n \\geq 2$. First, we consider the class $\\mathcal{A}$ of potentials $q(r)$ which can be extended analytically in $\\Re z \\geq 0$ such that $\\mid q(z)\\mid \\leq C \\ (1+ \\mid z \\mid )^{-\\rho}$, $\\rho \\textgreater{} \\frac{3}{2}$. If $q$ and $\\tilde{q}$ are two such potentials  and if the corresponding phase shifts $\\delta\\_l$ and $\\tilde{\\delta}\\_l$  are super-exponentially close, then $q=\\tilde{q}$. Secondly,\nwe study the class of potentials $q(r)$ which can be split into $q(r)=q\\_1(r) + q\\_2(r)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02276","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"}