{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IUIB4LGKBTSEVBEODQR7DG6IQY","short_pith_number":"pith:IUIB4LGK","schema_version":"1.0","canonical_sha256":"45101e2cca0ce44a848e1c23f19bc8861fa8d5b62047c0b38ddb7f64e796dd71","source":{"kind":"arxiv","id":"1606.03136","version":3},"attestation_state":"computed","paper":{"title":"Dynamical sampling and systems from iterative actions of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akram Aldroubi, Armenak Petrosyan","submitted_at":"2016-06-09T22:31:23Z","abstract_excerpt":"We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\\{A^ng: g\\in G,\\, n=0,1,2,\\dots \\}$, where $A$ is a bounded linear operators on a separable complex Hilbert space $ \\mathcal{H} $ and $G$ is a countable set of vectors in $ \\mathcal{H} $. The system of iterations mentioned above was motivated from the so called dynamical sampling problem. In dynamical sampling, an unknown function $f$ and its future states $A^nf$ are coarsely sampled at each time level $n$, $0\\leq n< L$, where $A$ is an evolution operator th"},"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":"1606.03136","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-09T22:31:23Z","cross_cats_sorted":[],"title_canon_sha256":"366f5744b4308286b82cf92f38df7901d77838e0a3d481e86edce45952871def","abstract_canon_sha256":"711c8720d06c66a25abc4bc1b6a9c792293dc1f543a3db5656c74624f3e6c72b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:52.897410Z","signature_b64":"1+FX3i1CUBuMd8YIfUvlB0919Em45kpSrm6gq2eb66r29M2kX7hP+CME8sPy14Lm2dVTZUSeV69BXWbyxwtbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45101e2cca0ce44a848e1c23f19bc8861fa8d5b62047c0b38ddb7f64e796dd71","last_reissued_at":"2026-05-18T01:00:52.896751Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:52.896751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamical sampling and systems from iterative actions of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Akram Aldroubi, Armenak Petrosyan","submitted_at":"2016-06-09T22:31:23Z","abstract_excerpt":"We review some of the recent developments and prove new results concerning frames and Bessel systems generated by iterations of the form $\\{A^ng: g\\in G,\\, n=0,1,2,\\dots \\}$, where $A$ is a bounded linear operators on a separable complex Hilbert space $ \\mathcal{H} $ and $G$ is a countable set of vectors in $ \\mathcal{H} $. The system of iterations mentioned above was motivated from the so called dynamical sampling problem. In dynamical sampling, an unknown function $f$ and its future states $A^nf$ are coarsely sampled at each time level $n$, $0\\leq n< L$, where $A$ is an evolution operator th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03136","kind":"arxiv","version":3},"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":"1606.03136","created_at":"2026-05-18T01:00:52.896847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03136v3","created_at":"2026-05-18T01:00:52.896847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03136","created_at":"2026-05-18T01:00:52.896847+00:00"},{"alias_kind":"pith_short_12","alias_value":"IUIB4LGKBTSE","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IUIB4LGKBTSEVBEO","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IUIB4LGK","created_at":"2026-05-18T12:30:22.444734+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.16949","citing_title":"Frames for source recovery from non-uniform dynamical samples","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY","json":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY.json","graph_json":"https://pith.science/api/pith-number/IUIB4LGKBTSEVBEODQR7DG6IQY/graph.json","events_json":"https://pith.science/api/pith-number/IUIB4LGKBTSEVBEODQR7DG6IQY/events.json","paper":"https://pith.science/paper/IUIB4LGK"},"agent_actions":{"view_html":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY","download_json":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY.json","view_paper":"https://pith.science/paper/IUIB4LGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03136&json=true","fetch_graph":"https://pith.science/api/pith-number/IUIB4LGKBTSEVBEODQR7DG6IQY/graph.json","fetch_events":"https://pith.science/api/pith-number/IUIB4LGKBTSEVBEODQR7DG6IQY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY/action/storage_attestation","attest_author":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY/action/author_attestation","sign_citation":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY/action/citation_signature","submit_replication":"https://pith.science/pith/IUIB4LGKBTSEVBEODQR7DG6IQY/action/replication_record"}},"created_at":"2026-05-18T01:00:52.896847+00:00","updated_at":"2026-05-18T01:00:52.896847+00:00"}