{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KRLJUFTOT6PRCWG7MQSVLXPXBB","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":"17032fc358054780bcdcbc838ab00c1283138edc6c21b099f12ccedbeb9d95f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-09T18:11:01Z","title_canon_sha256":"f97ac0b534eaa93e617552554b2b4658a263427ab5bf29d178ec1d31b1c8b807"},"schema_version":"1.0","source":{"id":"1411.2261","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2261","created_at":"2026-05-18T02:38:08Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2261v1","created_at":"2026-05-18T02:38:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2261","created_at":"2026-05-18T02:38:08Z"},{"alias_kind":"pith_short_12","alias_value":"KRLJUFTOT6PR","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KRLJUFTOT6PRCWG7","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KRLJUFTO","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:f7570bdbcf4e5fd74122cbb8990ae8663bfac8bded6b1d50c9c2a82da2e31f82","target":"graph","created_at":"2026-05-18T02:38:08Z","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":"In this paper, the problem of the order of approximation for the multivariate sampling Kantorovich operators is studied. The cases of the uniform approximation for uniformly continuous and bounded functions/signals belonging to Lipschitz classes and the case of the modular approximation for functions in Orlicz spaces are considered. In the latter context, Lipschitz classes of Zygmund-type which take into account of the modular functional involved are introduced. Applications to Lp(R^n), interpolation and exponential spaces can be deduced from the general theory formulated in the setting of Orl","authors_text":"Danilo Costarelli, Gianluca Vinti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-09T18:11:01Z","title":"Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2261","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":"sha256:4a1f74c0358833797faaac325e2225e6e31386f4a19f57c928e455c38bdb407f","target":"record","created_at":"2026-05-18T02:38:08Z","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":"17032fc358054780bcdcbc838ab00c1283138edc6c21b099f12ccedbeb9d95f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-11-09T18:11:01Z","title_canon_sha256":"f97ac0b534eaa93e617552554b2b4658a263427ab5bf29d178ec1d31b1c8b807"},"schema_version":"1.0","source":{"id":"1411.2261","kind":"arxiv","version":1}},"canonical_sha256":"54569a166e9f9f1158df642555ddf7087b0840593a9f65a82adcfabf4ea53975","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54569a166e9f9f1158df642555ddf7087b0840593a9f65a82adcfabf4ea53975","first_computed_at":"2026-05-18T02:38:08.002448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:08.002448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ga1a/A4PoGgyWJIAQZ8xcB7MGkm9GVSQO/HP15tIgw7tIv4AyHtvMimPbIyck7tvCM9Vm/ZMuFMGRgV/4MgKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:08.003041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2261","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a1f74c0358833797faaac325e2225e6e31386f4a19f57c928e455c38bdb407f","sha256:f7570bdbcf4e5fd74122cbb8990ae8663bfac8bded6b1d50c9c2a82da2e31f82"],"state_sha256":"124518013424e7dca83e361b3256c95cca89a706499bd73069c693273d5b7a52"}