{"paper":{"title":"Inverse scattering problem with fixed energy and fixed incident direction","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.G.Ramm","submitted_at":"2006-06-21T15:19:20Z","abstract_excerpt":"Let $A_q(\\alpha',\\alpha,k)$ be the scattering amplitude, corresponding to a local potential $q(x)$, $x\\in\\R^3$, $q(x)=0$ for $|x|>a$, where $a>0$ is a fixed number, $\\alpha',\\alpha\\in S^2$ are unit vectors, $S^2$ is the unit sphere in $\\R^3$, $\\alpha$ is the direction of the incident wave, $k^2>0$ is the energy. We prove that given an arbitrary function $f(\\alpha')\\in L^2(S^2)$, an arbitrary fixed $\\alpha_0\\in S^2$, an arbitrary fixed $k>0$, and an arbitrary small $\\ve>0$, there exists a potential $q(x)\\in L^2(D)$, where $D\\subset R^3$ is a bounded domain such that \\bee\n \\|A_q(\\alpha',\\alpha_0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0606055","kind":"arxiv","version":3},"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"}