{"paper":{"title":"Uncertainty principle and geometry of the infinite Grassmann manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Esteban Andruchow, Gustavo Corach","submitted_at":"2017-01-13T17:11:16Z","abstract_excerpt":"We study the pairs of projections $$ P_If=\\chi_If ,\\ \\ Q_Jf= \\left(\\chi_J \\hat{f}\\right)\\check{\\ } , \\ \\ f\\in L^2(\\mathbb{R}^n), $$ where $I, J\\subset \\mathbb{R}^n$ are sets of finite Lebesgue measure, $\\chi_I, \\chi_J$ denote the corresponding characteristic functions and $\\hat{\\ } , \\check{\\ }$ denote the Fourier-Plancherel transformation $L^2(\\mathbb{R}^n)\\to L^2(\\mathbb{R}^n)$ and its inverse. These pairs of projections have been widely studied by several authors in connection with the mathematical formulation of Heisenberg's uncertainty principle. Our study is done from a differential geom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03733","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"}