{"paper":{"title":"Completeness of the set $\\{e^{ik\\beta \\cdot s}\\}|_{\\forall \\beta \\in S^2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. G. Ramm","submitted_at":"2017-05-21T17:34:58Z","abstract_excerpt":"It is proved that the set $\\{e^{ik\\beta \\cdot s}\\}|_{\\forall \\beta \\in S^2}$, where $S^2$ is the unit sphere in $\\mathbb{R}^3$, $k>0$ is a fixed constant, $k^2$ is not a Dirichlet eigenvalue of the Laplacian in $D$, $s\\in S$, is total in $L^2(S)$. Here $S$ is a smooth, closed, connected surface in $\\mathbb{R}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00403","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"}