{"paper":{"title":"Fractional uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hugo Aimar, Ivana G\\'omez, Pablo Bolcatto","submitted_at":"2018-03-06T19:10:00Z","abstract_excerpt":"We use techniques of dyadic analysis in order to prove that, for every $0<s<\\tfrac{1}{2}$, there exists a positive constant $\\gamma(s)$ such that the inequality $$\\left(\\iint_{\\mathbb{R}^2}|x-y|^{2s-1}|\\varphi(x)||\\varphi(y)|dx dy\\right)\\left(\\iint_{\\mathbb{R}^2}|x-y|^{-2s-1}|\\varphi(x)-\\varphi(y)|^2 dx dy\\right)\\geq \\gamma(s)$$ holds for every $\\varphi$ with $||\\varphi||_{L^2(\\mathbb{R})}=1$. The second integral on the left hand side is the energy quadratic form of order $s$, which for the limit case $s=1$ gives the local form $Var|\\hat{\\varphi}|^2$ or $\\int|\\nabla\\varphi|^2$. The first is a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02384","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"}