{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VAFQFL2LU5JCZFWI377USZZO7H","short_pith_number":"pith:VAFQFL2L","schema_version":"1.0","canonical_sha256":"a80b02af4ba7522c96c8dfff49672ef9e3b065785bad11c84a9225c15ff2c570","source":{"kind":"arxiv","id":"1410.1828","version":1},"attestation_state":"computed","paper":{"title":"Sampling and Galerkin reconstruction in reproducing kernel spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Cheng cheng, Qiyu Sun, Yingchun Jiang","submitted_at":"2014-10-07T18:08:25Z","abstract_excerpt":"In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation."},"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":"1410.1828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-10-07T18:08:25Z","cross_cats_sorted":["math.IT","math.NA"],"title_canon_sha256":"c8491f41e9936cf79dacc736f0dd6784efc868c39e69744f6f49c1bdab8d29eb","abstract_canon_sha256":"415c89b30b430259b18ee59ad036328f2f2cef0ffd41093bc981d44f3d659f0d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:54.657177Z","signature_b64":"HlLmsItPzl0ixmEba70X7ZiGxrzk++d5tZS36onk8Y/5BMV+n3SFg+Wb5l8NoJXiFwODObs0p4ng9weTpV/OCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a80b02af4ba7522c96c8dfff49672ef9e3b065785bad11c84a9225c15ff2c570","last_reissued_at":"2026-05-18T02:40:54.656654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:54.656654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling and Galerkin reconstruction in reproducing kernel spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Cheng cheng, Qiyu Sun, Yingchun Jiang","submitted_at":"2014-10-07T18:08:25Z","abstract_excerpt":"In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1828","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":"1410.1828","created_at":"2026-05-18T02:40:54.656729+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.1828v1","created_at":"2026-05-18T02:40:54.656729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1828","created_at":"2026-05-18T02:40:54.656729+00:00"},{"alias_kind":"pith_short_12","alias_value":"VAFQFL2LU5JC","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VAFQFL2LU5JCZFWI","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VAFQFL2L","created_at":"2026-05-18T12:28:52.271510+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/VAFQFL2LU5JCZFWI377USZZO7H","json":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H.json","graph_json":"https://pith.science/api/pith-number/VAFQFL2LU5JCZFWI377USZZO7H/graph.json","events_json":"https://pith.science/api/pith-number/VAFQFL2LU5JCZFWI377USZZO7H/events.json","paper":"https://pith.science/paper/VAFQFL2L"},"agent_actions":{"view_html":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H","download_json":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H.json","view_paper":"https://pith.science/paper/VAFQFL2L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.1828&json=true","fetch_graph":"https://pith.science/api/pith-number/VAFQFL2LU5JCZFWI377USZZO7H/graph.json","fetch_events":"https://pith.science/api/pith-number/VAFQFL2LU5JCZFWI377USZZO7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H/action/storage_attestation","attest_author":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H/action/author_attestation","sign_citation":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H/action/citation_signature","submit_replication":"https://pith.science/pith/VAFQFL2LU5JCZFWI377USZZO7H/action/replication_record"}},"created_at":"2026-05-18T02:40:54.656729+00:00","updated_at":"2026-05-18T02:40:54.656729+00:00"}