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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.05622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-19T14:48:20Z","cross_cats_sorted":[],"title_canon_sha256":"11bfbd58784b1eb612b5d502e54c8927dd4b676d16eea77fbc9d69db9f9e8ad1","abstract_canon_sha256":"4969db2e302b0da3d0fbe00bd9d2fcbe9ed1a101fa1666f96809ec851876ea43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.182389Z","signature_b64":"kM1gA/HCblyzhUDnIXQtnhKoUlhqLXL/caaQZ7pi1syV7fLlX9pU63u0mi6PKge/MNbMHjN/TcBHtteS48/PDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f3556f213ca31c4e1418c96208dd2512e110585e8a72548670d2dd4707157eb","last_reissued_at":"2026-05-18T00:56:06.181802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.181802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $G \\subset \\cH$. 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