{"paper":{"title":"Operator representations of frames: boundedness, duality, and stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marzieh Hasannasab, Ole Christensen","submitted_at":"2017-04-28T13:14:24Z","abstract_excerpt":"The purpose of the paper is to analyze frames $\\{f_k\\}_{k\\in \\mathbf Z}$ having the form $\\{T^kf_0\\}_{k\\in\\mathbf Z}$ for some linear operator $T: \\mbox{span} \\{f_k\\}_{k\\in \\mathbf Z} \\to \\mbox{span}\\{f_k\\}_{k\\in \\mathbf Z}$. A key result characterizes boundedness of the operator $T$ in terms of shift-invariance of a certain sequence space. One of the consequences is a characterization of the case where the representation $\\{f_k\\}_{k\\in \\mathbf Z}=\\{T^kf_0\\}_{k\\in\\mathbf Z}$ can be achieved for an operator $T$ that has an extension to a bounded bijective operator $\\widetilde{T}: \\cal H \\to \\ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08918","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"}