{"paper":{"title":"Inverse scattering with the data at fixed energy and fixed incident direction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.G.Ramm","submitted_at":"2013-02-02T16:00:30Z","abstract_excerpt":"Consider the Schr\\\"odinger operator $-\\nabla^2+q$ $ $q$, $q=q(x), x \\in \\mathbf{R}^3$. Let $A(\\beta,\\alpha, k)$ be the corresponding scattering amplitude, $k^2$ be the energy, $\\alpha \\in S^2$ be the incident direction, $\\beta \\in S^2$ be the direction of scattered wave, $S^2$ be the unit sphere in $\\mathbf{R}^3$. Assume that $k=k_0 >0$ is fixed, and $\\alpha=\\alpha_0$ is fixed. Then the scattering data are $A(\\beta)= A(\\beta,\\alpha_0, k_0)=A_q(\\beta)$ is a function on $S^2$. The following invers$ \\textit{IP: Given an arbitrary $f \\in L^2(S^2)$ and an arbitrary small number $$ $q \\in C_0^{\\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5000","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"}