{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FNAXTKBYIPJOLU57ADAQ2BPXQD","short_pith_number":"pith:FNAXTKBY","schema_version":"1.0","canonical_sha256":"2b4179a83843d2e5d3bf00c10d05f780dde8c08b95cc0b16791f67202f923340","source":{"kind":"arxiv","id":"1009.4389","version":1},"attestation_state":"computed","paper":{"title":"B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinh D\\~ung","submitted_at":"2010-09-22T15:29:00Z","abstract_excerpt":"Let $\\xi = \\{x^j\\}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\\II}^d:=[0,1]^d$, and $\\Phi = \\{\\phi_j\\}_{j =1}^n$ a family of $n$ functions on ${\\II}^d$. We define the linear sampling algorithm $L_n(\\Phi,\\xi,\\cdot)$ for an approximate recovery of a continuous function $f$ on ${\\II}^d$ from the sampled values $f(x^1), ..., f(x^n)$, by $$L_n(\\Phi,\\xi,f)\\ := \\ \\sum_{j=1}^n f(x^j)\\phi_j$$.\n  For the Besov class $B^\\alpha_{p,\\theta}$ of mixed smoothness $\\alpha$ (defined as the unit ball of the Besov space $\\MB$), to study optimality of $L_n(\\Phi,\\xi,\\cdot)$ in $L_q({\\II}^d)$ we use the quan"},"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":"1009.4389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-09-22T15:29:00Z","cross_cats_sorted":[],"title_canon_sha256":"9c4fdafbec558aca8f33eebf4c78db0806b11ec92a3ba4d5587d38e9afc0358a","abstract_canon_sha256":"2a93ff8080ab61c374c5d199a59580f283fce08fa6caf58c3f6e76cb157ec51a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:33.234389Z","signature_b64":"wfewSuJ6JBXCP+ToUeCSMn3xlYpZoIMGW0oUvqI4Pt3bP08UDVQxPyujzCrxYiyNDjn1E24zvPXJ94hOADLyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b4179a83843d2e5d3bf00c10d05f780dde8c08b95cc0b16791f67202f923340","last_reissued_at":"2026-05-18T04:40:33.233847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:33.233847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinh D\\~ung","submitted_at":"2010-09-22T15:29:00Z","abstract_excerpt":"Let $\\xi = \\{x^j\\}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\\II}^d:=[0,1]^d$, and $\\Phi = \\{\\phi_j\\}_{j =1}^n$ a family of $n$ functions on ${\\II}^d$. We define the linear sampling algorithm $L_n(\\Phi,\\xi,\\cdot)$ for an approximate recovery of a continuous function $f$ on ${\\II}^d$ from the sampled values $f(x^1), ..., f(x^n)$, by $$L_n(\\Phi,\\xi,f)\\ := \\ \\sum_{j=1}^n f(x^j)\\phi_j$$.\n  For the Besov class $B^\\alpha_{p,\\theta}$ of mixed smoothness $\\alpha$ (defined as the unit ball of the Besov space $\\MB$), to study optimality of $L_n(\\Phi,\\xi,\\cdot)$ in $L_q({\\II}^d)$ we use the quan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4389","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":"1009.4389","created_at":"2026-05-18T04:40:33.233935+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4389v1","created_at":"2026-05-18T04:40:33.233935+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4389","created_at":"2026-05-18T04:40:33.233935+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNAXTKBYIPJO","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNAXTKBYIPJOLU57","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNAXTKBY","created_at":"2026-05-18T12:26:07.630475+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/FNAXTKBYIPJOLU57ADAQ2BPXQD","json":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD.json","graph_json":"https://pith.science/api/pith-number/FNAXTKBYIPJOLU57ADAQ2BPXQD/graph.json","events_json":"https://pith.science/api/pith-number/FNAXTKBYIPJOLU57ADAQ2BPXQD/events.json","paper":"https://pith.science/paper/FNAXTKBY"},"agent_actions":{"view_html":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD","download_json":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD.json","view_paper":"https://pith.science/paper/FNAXTKBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4389&json=true","fetch_graph":"https://pith.science/api/pith-number/FNAXTKBYIPJOLU57ADAQ2BPXQD/graph.json","fetch_events":"https://pith.science/api/pith-number/FNAXTKBYIPJOLU57ADAQ2BPXQD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD/action/storage_attestation","attest_author":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD/action/author_attestation","sign_citation":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD/action/citation_signature","submit_replication":"https://pith.science/pith/FNAXTKBYIPJOLU57ADAQ2BPXQD/action/replication_record"}},"created_at":"2026-05-18T04:40:33.233935+00:00","updated_at":"2026-05-18T04:40:33.233935+00:00"}