{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:JMEGRUY6JHPSGAPEL65YBWKL3L","short_pith_number":"pith:JMEGRUY6","schema_version":"1.0","canonical_sha256":"4b0868d31e49df2301e45fbb80d94bdaee45f6e9e904883ce522766f1a7a3ac3","source":{"kind":"arxiv","id":"0904.4716","version":2},"attestation_state":"computed","paper":{"title":"Sampling Theorem and Discrete Fourier Transform on the Hyperboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Juan Carlos S\\'anchez-Monreal, Julio Guerrero, Manuel Calixto","submitted_at":"2009-04-29T22:54:30Z","abstract_excerpt":"Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from $N$ samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from $N$ samples is still possible and the accuracy of the approximat"},"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":"0904.4716","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-04-29T22:54:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"22dc43f816efeaa5040df6132668872cd0a27c9feadb1dd1d2fe14a8ae147411","abstract_canon_sha256":"7054114113592e25dc5e60a399a294e32c82670380ebf1358b198e6e76056803"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:45.989573Z","signature_b64":"i09A/JTABadNmxwcW/JkNs9L6UIDMkAHURS5dnfoxnwYbu1rqq06KeCjSLrfao0qzR6DbBUNwsjAcXPH5vfBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0868d31e49df2301e45fbb80d94bdaee45f6e9e904883ce522766f1a7a3ac3","last_reissued_at":"2026-05-18T04:13:45.989125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:45.989125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling Theorem and Discrete Fourier Transform on the Hyperboloid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Juan Carlos S\\'anchez-Monreal, Julio Guerrero, Manuel Calixto","submitted_at":"2009-04-29T22:54:30Z","abstract_excerpt":"Using Coherent-State (CS) techniques, we prove a sampling theorem for holomorphic functions on the hyperboloid (or its stereographic projection onto the open unit disk $\\mathbb D_1$), seen as a homogeneous space of the pseudo-unitary group SU(1,1). We provide a reconstruction formula for bandlimited functions, through a sinc-type kernel, and a discrete Fourier transform from $N$ samples properly chosen. We also study the case of undersampling of band-unlimited functions and the conditions under which a partial reconstruction from $N$ samples is still possible and the accuracy of the approximat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4716","kind":"arxiv","version":2},"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":"0904.4716","created_at":"2026-05-18T04:13:45.989220+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.4716v2","created_at":"2026-05-18T04:13:45.989220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4716","created_at":"2026-05-18T04:13:45.989220+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMEGRUY6JHPS","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMEGRUY6JHPSGAPE","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMEGRUY6","created_at":"2026-05-18T12:26:00.592388+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/JMEGRUY6JHPSGAPEL65YBWKL3L","json":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L.json","graph_json":"https://pith.science/api/pith-number/JMEGRUY6JHPSGAPEL65YBWKL3L/graph.json","events_json":"https://pith.science/api/pith-number/JMEGRUY6JHPSGAPEL65YBWKL3L/events.json","paper":"https://pith.science/paper/JMEGRUY6"},"agent_actions":{"view_html":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L","download_json":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L.json","view_paper":"https://pith.science/paper/JMEGRUY6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.4716&json=true","fetch_graph":"https://pith.science/api/pith-number/JMEGRUY6JHPSGAPEL65YBWKL3L/graph.json","fetch_events":"https://pith.science/api/pith-number/JMEGRUY6JHPSGAPEL65YBWKL3L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L/action/storage_attestation","attest_author":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L/action/author_attestation","sign_citation":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L/action/citation_signature","submit_replication":"https://pith.science/pith/JMEGRUY6JHPSGAPEL65YBWKL3L/action/replication_record"}},"created_at":"2026-05-18T04:13:45.989220+00:00","updated_at":"2026-05-18T04:13:45.989220+00:00"}