{"paper":{"title":"Uncertainty Principles for Compact Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GM","math.GR"],"primary_cat":"math.RT","authors_text":"Alexander Russell, Gorjan Alagic","submitted_at":"2006-08-28T23:06:16Z","abstract_excerpt":"We establish an operator-theoretic uncertainty principle over arbitrary compact groups, generalizing several previous results. As a consequence, we show that if f is in L^2(G), then the product of the measures of the supports of f and its Fourier transform ^f is at least 1; here, the dual measure is given by the sum, over all irreducible representations V, of d_V rank(^f(V)). For finite groups, our principle implies the following: if P and R are projection operators on the group algebra C[G] such that P commutes with projection onto each group element, and R commutes with left multiplication, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608702","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"}