{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:5AEGOHOXJO56RBPIBT3M5HDMFL","short_pith_number":"pith:5AEGOHOX","schema_version":"1.0","canonical_sha256":"e808671dd74bbbe885e80cf6ce9c6c2af3a7dbe6b3023413ac282620de9f09b7","source":{"kind":"arxiv","id":"1407.0321","version":1},"attestation_state":"computed","paper":{"title":"Multivariate exact and falsified sampling approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Krivoshein, M. Skopina","submitted_at":"2014-07-01T17:08:03Z","abstract_excerpt":"Approximation properties of the expansions $\\sum_{k\\in{\\mathbb z}^d}c_k\\phi(M^jx+k)$, where $M$ is a matrix dilation, $c_k$ is either the sampled value of a signal $f$ at $M^{-j}k$ or the integral average of $f$ near $M^{-j}k$ (falsified sampled value), are studied. Error estimations in $L_p$-norm, $2\\le p\\le\\infty$, are given in terms of the Fourier transform of $f$. The approximation order depends on how smooth is $f$, on the order of Strang-Fix condition for $\\phi$ and on $M$. Some special properties of $\\phi$ are\n  required. To estimate the approximation order of falsified sampling expansi"},"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":"1407.0321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-01T17:08:03Z","cross_cats_sorted":[],"title_canon_sha256":"b8b454cc1920516dcd592262966136204deb1e83aa5fe7508d2399466c97e2c2","abstract_canon_sha256":"a48789c608e05e1a8f36d2a3a59ab8445f342807a4c16ea3d74d23c6fd80db5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:34.345881Z","signature_b64":"Ov6rt+DtBZwyq77UD3TloSAT4AQpngHAw9drv+sjKbesA9dw7W4c8MlFQjZLMz9cwZCHpqrrJnFl1Y4wGbXEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e808671dd74bbbe885e80cf6ce9c6c2af3a7dbe6b3023413ac282620de9f09b7","last_reissued_at":"2026-05-18T02:48:34.345110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:34.345110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multivariate exact and falsified sampling approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Krivoshein, M. Skopina","submitted_at":"2014-07-01T17:08:03Z","abstract_excerpt":"Approximation properties of the expansions $\\sum_{k\\in{\\mathbb z}^d}c_k\\phi(M^jx+k)$, where $M$ is a matrix dilation, $c_k$ is either the sampled value of a signal $f$ at $M^{-j}k$ or the integral average of $f$ near $M^{-j}k$ (falsified sampled value), are studied. Error estimations in $L_p$-norm, $2\\le p\\le\\infty$, are given in terms of the Fourier transform of $f$. The approximation order depends on how smooth is $f$, on the order of Strang-Fix condition for $\\phi$ and on $M$. Some special properties of $\\phi$ are\n  required. To estimate the approximation order of falsified sampling expansi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0321","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":"1407.0321","created_at":"2026-05-18T02:48:34.345224+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.0321v1","created_at":"2026-05-18T02:48:34.345224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0321","created_at":"2026-05-18T02:48:34.345224+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AEGOHOXJO56","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AEGOHOXJO56RBPI","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AEGOHOX","created_at":"2026-05-18T12:28:14.216126+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/5AEGOHOXJO56RBPIBT3M5HDMFL","json":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL.json","graph_json":"https://pith.science/api/pith-number/5AEGOHOXJO56RBPIBT3M5HDMFL/graph.json","events_json":"https://pith.science/api/pith-number/5AEGOHOXJO56RBPIBT3M5HDMFL/events.json","paper":"https://pith.science/paper/5AEGOHOX"},"agent_actions":{"view_html":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL","download_json":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL.json","view_paper":"https://pith.science/paper/5AEGOHOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.0321&json=true","fetch_graph":"https://pith.science/api/pith-number/5AEGOHOXJO56RBPIBT3M5HDMFL/graph.json","fetch_events":"https://pith.science/api/pith-number/5AEGOHOXJO56RBPIBT3M5HDMFL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL/action/storage_attestation","attest_author":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL/action/author_attestation","sign_citation":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL/action/citation_signature","submit_replication":"https://pith.science/pith/5AEGOHOXJO56RBPIBT3M5HDMFL/action/replication_record"}},"created_at":"2026-05-18T02:48:34.345224+00:00","updated_at":"2026-05-18T02:48:34.345224+00:00"}