{"paper":{"title":"A dynamical system approach to Heisenberg Uniqueness Pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Karim Kellay (IMB), Philippe Jaming (IMB)","submitted_at":"2013-12-21T10:59:24Z","abstract_excerpt":"Let $\\Lambda$ be a set of lines in $\\mathbb{R}^2$ that intersect at the origin. For $\\Gamma\\subset\\mathbb{R}^2$ a smooth curve, we denote by $\\mathcal{A}\\mathcal{C}(\\Gamma)$ the subset of finite measures on $\\Gamma$ that are absolutely continuous with respect to arc length on $\\Gamma$. For such a $\\mu$, $\\widehat{\\mu}$ denotes the Fourier transform of $\\mu$. Following Hendenmalm and Montes-Rodr\\'iguez, we will say that $(\\Gamma,\\Lambda)$ is a Heisenberg Uniqueness Pair if $\\mu\\in\\mathcal{A}\\mathcal{C}(\\Gamma)$ is such that $\\widehat{\\mu}=0$ on $\\Lambda$, then $\\mu=0$. The aim of this paper is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6236","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"}