{"paper":{"title":"Gabor frames with rational density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Preben Gr{\\aa}berg Nes, Yurii Lyubarskii","submitted_at":"2011-08-12T18:34:06Z","abstract_excerpt":"We consider the frame property of the Gabor system G(g, {\\alpha}, {\\beta}) = {e2{\\pi}i{\\beta}nt g(t - {\\alpha}m) : m, n \\in Z} for the case of rational oversampling, i.e. {\\alpha}, {\\beta} \\in Q. A 'rational' analogue of the Ron-Shen Gramian is constructed, and prove that for any odd window function g the system G(g, {\\alpha}, {\\beta}) does not generate a frame if {\\alpha}{\\beta} = (n-1)/n. Special attention is paid to the first Hermite function h_1(t) = te^(-{\\pi}t^2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2684","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"}