{"paper":{"title":"Heisenberg uniqueness pairs for some algebraic curves and surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Deb Kumar Giri, R. K. Srivastava","submitted_at":"2016-05-22T01:13:17Z","abstract_excerpt":"Let $X(\\Gamma)$ be the space of all finite Borel measure $\\mu$ in $\\mathbb R^2$ which is supported on the curve $\\Gamma$ and absolutely continuous with respect to the arc length of $\\Gamma$. For $\\Lambda\\subset\\mathbb R^2,$ the pair $\\left(\\Gamma, \\Lambda\\right)$ is called a Heisenberg uniqueness pair for $X(\\Gamma)$ if any $\\mu\\in X(\\Gamma)$ satisfies $\\hat\\mu\\vert_\\Lambda=0,$ implies $\\mu=0.$ We explore the Heisenberg uniqueness pairs corresponding to the cross, exponential curves, and surfaces. Then, we prove a characterization of the Heisenberg uniqueness pairs corresponding to finitely ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06724","kind":"arxiv","version":6},"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"}