{"paper":{"title":"Weaving Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Karlheinz Gr\\\"ochenig, Mark C. Lammers, Peter G. Casazza, Richard G. Lynch, Travis Bemrose","submitted_at":"2015-03-13T03:59:43Z","abstract_excerpt":"We study an intriguing question in frame theory we call \"Weaving Frames\" that is partially motivated by preprocessing of Gabor frames. Two frames $\\{\\varphi_i\\}_{i\\in I}$ and $\\{\\psi_i \\}_{i\\in I}$ for a Hilbert space ${\\mathbb H}$ are woven if there are constants $0<A \\le B $ so that for every subset $\\sigma \\subset I$, the family $\\{\\varphi_i\\}_{i\\in \\sigma} \\cup \\{\\psi_i\\}_{i\\in \\sigma^c}$ is a frame for $\\mathbb H$ with frame bounds $A,B$. Fundamental properties of woven frames are developed and key differences between weaving Riesz bases and weaving frames are considered. In particular, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03947","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"}