{"paper":{"title":"Scalability of frames generated by dynamical operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Roza Aceska, Yeon Hyang Kim","submitted_at":"2016-08-19T14:48:20Z","abstract_excerpt":"Let $A$ be an operator on {a separable } Hilbert space $\\cH$, and let $G \\subset \\cH$. It is known that - under appropriate conditions on $A$ and $G$ - the set of iterations $F_G(A)= \\{A^j \\gbf \\; | \\; \\gbf \\in G, \\; 0 \\leq j \\leq L(\\gbf) \\} $ is a frame for $\\cH$. We call $F_G(A)$ a dynamical frame for $\\cH$, and explore further its properties; in particular, we show that the canonical dual frame of $F_G(A)$ also has an iterative set structure.\n  We explore the relations between the operator $A$, the set $G$ and the number of iterations $L$ which ensure that the system $F_G(A)$ is a scalable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05622","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":""},"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"}