{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FSD4FQEQ7JYNKBQVDJZ62TUUTB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b48a8b4a3bf8eca7b899a59c616964cb91865a8da10ae07754d7358d8f5abe9b","cross_cats_sorted":["math.FA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-02T17:28:06Z","title_canon_sha256":"ed87e3bf01a66ff196a3ec365df4d42f3491e1086ef8f30545c1e6100393512e"},"schema_version":"1.0","source":{"id":"1503.00628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00628","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00628v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00628","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"FSD4FQEQ7JYN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FSD4FQEQ7JYNKBQV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FSD4FQEQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:3851e63c0cfba3c99d89c8401bb40470f08d27197f45cac11c95a454530e5d71","target":"graph","created_at":"2026-05-18T02:25:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the recovery of operators with bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as operator sampling. Kailath, and later Kozek and the authors have shown that operator sampling is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the sampling rate that depend on size and geometry of the","authors_text":"David F. Walnut, G\\\"otz E. Pfander","cross_cats":["math.FA","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-02T17:28:06Z","title":"Sampling and reconstruction of operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00628","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9e351660d749752a8e28a63b11d1bbfcfbd884a7430b43da0f3b7d86c2ab034a","target":"record","created_at":"2026-05-18T02:25:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b48a8b4a3bf8eca7b899a59c616964cb91865a8da10ae07754d7358d8f5abe9b","cross_cats_sorted":["math.FA","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-03-02T17:28:06Z","title_canon_sha256":"ed87e3bf01a66ff196a3ec365df4d42f3491e1086ef8f30545c1e6100393512e"},"schema_version":"1.0","source":{"id":"1503.00628","kind":"arxiv","version":1}},"canonical_sha256":"2c87c2c090fa70d506151a73ed4e949863a94b0b315628124b89509b495f3472","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c87c2c090fa70d506151a73ed4e949863a94b0b315628124b89509b495f3472","first_computed_at":"2026-05-18T02:25:49.630742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:49.630742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yDVPE86rBGldA0oyH9Ucm30SuNdaCK3+6IqVpObXjn1glTCK+EE2mg/WmuTO/QfnNtpuLhJSMt4yBiZjxfXMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:49.631123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e351660d749752a8e28a63b11d1bbfcfbd884a7430b43da0f3b7d86c2ab034a","sha256:3851e63c0cfba3c99d89c8401bb40470f08d27197f45cac11c95a454530e5d71"],"state_sha256":"f12caffb957c9c51bbf60b57f1dbf5788b41c4333d7c0840e75414a617c4b016"}