{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:YU5RBJQ336TR6QONFKXGCN52JO","short_pith_number":"pith:YU5RBJQ3","schema_version":"1.0","canonical_sha256":"c53b10a61bdfa71f41cd2aae6137ba4bb0d4dab0ef78ff0c3d05226e3b4d61d6","source":{"kind":"arxiv","id":"1803.08466","version":1},"attestation_state":"computed","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 ${\\"},"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":"1803.08466","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-03-22T17:07:12Z","cross_cats_sorted":[],"title_canon_sha256":"872fb83e55f484ff84b6ae1b993c9535e188bab96ed148e0765a48e97785fc78","abstract_canon_sha256":"50832b7af84d6f484b4bb88f1a2a3e4c14528c3a5333d1b01ff1755f1a4a6d29"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:22.762383Z","signature_b64":"gzccn/mNqTHTDS4hmFySRvp6TKRVQI6HnvsyZwz0lh2bgzMVmcueuopS4KX43pQjT2rgaK5B+KtiUc2zzsGkDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c53b10a61bdfa71f41cd2aae6137ba4bb0d4dab0ef78ff0c3d05226e3b4d61d6","last_reissued_at":"2026-05-18T00:20:22.761725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:22.761725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.08466","created_at":"2026-05-18T00:20:22.761835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.08466v1","created_at":"2026-05-18T00:20:22.761835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.08466","created_at":"2026-05-18T00:20:22.761835+00:00"},{"alias_kind":"pith_short_12","alias_value":"YU5RBJQ336TR","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_16","alias_value":"YU5RBJQ336TR6QON","created_at":"2026-05-18T12:33:04.347982+00:00"},{"alias_kind":"pith_short_8","alias_value":"YU5RBJQ3","created_at":"2026-05-18T12:33:04.347982+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO","json":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO.json","graph_json":"https://pith.science/api/pith-number/YU5RBJQ336TR6QONFKXGCN52JO/graph.json","events_json":"https://pith.science/api/pith-number/YU5RBJQ336TR6QONFKXGCN52JO/events.json","paper":"https://pith.science/paper/YU5RBJQ3"},"agent_actions":{"view_html":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO","download_json":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO.json","view_paper":"https://pith.science/paper/YU5RBJQ3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.08466&json=true","fetch_graph":"https://pith.science/api/pith-number/YU5RBJQ336TR6QONFKXGCN52JO/graph.json","fetch_events":"https://pith.science/api/pith-number/YU5RBJQ336TR6QONFKXGCN52JO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO/action/storage_attestation","attest_author":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO/action/author_attestation","sign_citation":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO/action/citation_signature","submit_replication":"https://pith.science/pith/YU5RBJQ336TR6QONFKXGCN52JO/action/replication_record"}},"created_at":"2026-05-18T00:20:22.761835+00:00","updated_at":"2026-05-18T00:20:22.761835+00:00"}