{"paper":{"title":"Dynamical sampling and frame representations with bounded operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ehsan Rashidi, Marzieh Hasannasab, Ole Christensen","submitted_at":"2018-03-22T17:07:12Z","abstract_excerpt":"The purpose of this paper is to study frames for a Hilbert space ${\\cal H},$ having the form $\\{T^n \\varphi\\}_{n=0}^\\infty$ for some $\\varphi \\in {\\cal H}$ and an operator $T: {\\cal H} \\to {\\cal H}.$ We characterize the frames that have such a representation for a bounded operator $T,$ and discuss the properties of this operator. In particular, we prove that the image chain of $T$ has finite length $N$ in the overcomplete case; furthermore $\\{T^n \\varphi\\}_{n=0}^\\infty$ has the very particular property that $\\{T^n \\varphi\\}_{n=0}^{N-1} \\cup \\{T^n \\varphi\\}_{n=N+\\ell}^\\infty$ is a frame for ${\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.08466","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"}