{"paper":{"title":"On Beurling's uncertainty principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Xin Gao","submitted_at":"2015-06-17T05:17:02Z","abstract_excerpt":"We generalise a result of Hedenmalm to show that if a function $f$ on $\\mathbb{R}$ is such that $\\int_{\\mathbb{R}^2} \\bigl|f(x) \\, \\hat f(y)\\bigr| \\,e^{\\lambda \\left|xy\\right|} \\,dx\\,dy = O( (1-\\lambda)^{-N} )$ as $\\lambda \\to 1-$, then $f$ is the product of a polynomial and a gaussian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05209","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"}