{"paper":{"title":"Fourier nonuniqueness sets for the hyperbola and the Perron-Frobenius operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.CA","authors_text":"Deb Kumar Giri","submitted_at":"2020-09-20T20:21:36Z","abstract_excerpt":"Let $\\Gamma$ be a smooth curve or finite disjoint union of smooth curves in the plane and $\\Lambda$ be any subset of the plane. Let $\\mathcal X(\\Gamma)$ be the space of all finite complex-valued Borel measures in the plane which are supported on $\\Gamma$ and are absolutely continuous with respect to the arc length measure on $\\Gamma.$ Let $\\mathcal{AC}(\\Gamma,\\Lambda)=\\{\\mu\\in \\mathcal{X}(\\Gamma) : \\hat\\mu|_{\\Lambda}=0\\},$ then we prove the following results: \\begin{enumerate}[(a)] \\item For a rational perturbation of $\\Lambda_\\beta$ namely, $\\Lambda_\\beta^\\theta=\\left((\\mathbb Z+\\{\\theta\\})\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.09516","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.09516/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}