{"paper":{"title":"Balian-Low type theorems on homogeneous groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Rottensteiner, Jordy Timo van Velthoven, Jos\\'e Luis Romero, Karlheinz Gr\\\"ochenig","submitted_at":"2019-08-08T13:16:45Z","abstract_excerpt":"We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(\\pi, \\mathcal{H}_{\\pi})$ be an irreducible, square-integrable representation modulo the center $Z(N)$ of $N$ on a Hilbert space $\\mathcal{H}_{\\pi}$ of formal dimension $d_\\pi $. If $g \\in \\mathcal{H}_{\\pi}$ is an integrable vector and the set $\\{ \\pi (\\lambda )g : \\lambda \\in \\Lambda \\}$ for a discrete subset $\\Lambda \\subseteq N / Z(N)$ forms a frame for $\\mathcal{H}_{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}