{"paper":{"title":"Uncertainty principle on weighted spheres, balls and simplexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yuan Xu","submitted_at":"2013-04-22T23:26:43Z","abstract_excerpt":"For a family of weight functions $h_\\kappa$ that are invariant under a reflection group, the uncertainty principle on the unit sphere in the form of $$\n  \\min_{1 \\le i \\le d} \\int_{\\mathbb{S}^{d-1}} (1- x_i) |f(x)|^2 h_\\kappa^2(x) d\\sigma \\int_{\\mathbb{S}^{d-1}}\\left |\\nabla_0 f(x)\\right |^2 h_\\kappa^2(x) d\\sigma \\ge c $$ is established for invariant functions $f$ that have unit norm and zero mean, where $\\nabla_0$ is the spherical gradient. In the same spirit, uncertainty principles for weighted spaces on the unit ball and on the standard simplex are established, some of them hold for all adm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6135","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"}