{"paper":{"title":"Group Riesz and Frame Sequences: The Bracket and the Gramian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Davide Barbieri, Eugenio Hernandez, Victoria Paternostro","submitted_at":"2016-08-09T11:36:43Z","abstract_excerpt":"Given a discrete group and a unitary representation on a Hilbert space $\\mathcal{H}$, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of $\\mathcal{H}$. As a consequence, combining this result with known frame theory, we can recover in a simple way all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02767","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"}