{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GBR7TU3GDIUXDLQUNDXVUTLOV5","short_pith_number":"pith:GBR7TU3G","schema_version":"1.0","canonical_sha256":"3063f9d3661a2971ae1468ef5a4d6eaf421f8f45b2c46a2fbc498f8a5ecdd221","source":{"kind":"arxiv","id":"1104.0615","version":2},"attestation_state":"computed","paper":{"title":"An orthogonal polynomial analogue of the Landau-Pollak-Slepian time-frequency analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Wolfgang Erb","submitted_at":"2011-04-04T16:31:01Z","abstract_excerpt":"The aim of this article is to present a time-frequency theory for orthogonal polynomials on the interval [-1,1] that runs parallel to the time-frequency analysis of bandlimited functions developed by Landau, Pollak and Slepian. For this purpose, the spectral decomposition of a particular compact time-frequency-operator is studied. This decomposition and its eigenvalues are closely related to the theory of orthogonal polynomials. Results from both theories, the theory of orthogonal polynomials and the Landau-Pollak-Slepian theory, can be used to prove localization and approximation properties o"},"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":"1104.0615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-04T16:31:01Z","cross_cats_sorted":[],"title_canon_sha256":"79693dd504fc23233f8cf44a9ed443a80efa3453375a25c6a648ab70f8b99dee","abstract_canon_sha256":"d150d27c88f097a87dfc7a93fe4f4fdede704f827f79833331422285c1c4a8eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:02.784046Z","signature_b64":"z+jCP7j1cPOIkMVSNE04/kSnTalQKjb4cFnAZ8xWSwsNtjU82oXZjYUOEOF7FGdP1AGn3qJfuq8+sAyNavJSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3063f9d3661a2971ae1468ef5a4d6eaf421f8f45b2c46a2fbc498f8a5ecdd221","last_reissued_at":"2026-05-18T04:00:02.783221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:02.783221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An orthogonal polynomial analogue of the Landau-Pollak-Slepian time-frequency analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Wolfgang Erb","submitted_at":"2011-04-04T16:31:01Z","abstract_excerpt":"The aim of this article is to present a time-frequency theory for orthogonal polynomials on the interval [-1,1] that runs parallel to the time-frequency analysis of bandlimited functions developed by Landau, Pollak and Slepian. For this purpose, the spectral decomposition of a particular compact time-frequency-operator is studied. This decomposition and its eigenvalues are closely related to the theory of orthogonal polynomials. Results from both theories, the theory of orthogonal polynomials and the Landau-Pollak-Slepian theory, can be used to prove localization and approximation properties o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0615","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":"1104.0615","created_at":"2026-05-18T04:00:02.783365+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.0615v2","created_at":"2026-05-18T04:00:02.783365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0615","created_at":"2026-05-18T04:00:02.783365+00:00"},{"alias_kind":"pith_short_12","alias_value":"GBR7TU3GDIUX","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"GBR7TU3GDIUXDLQU","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"GBR7TU3G","created_at":"2026-05-18T12:26:28.662955+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/GBR7TU3GDIUXDLQUNDXVUTLOV5","json":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5.json","graph_json":"https://pith.science/api/pith-number/GBR7TU3GDIUXDLQUNDXVUTLOV5/graph.json","events_json":"https://pith.science/api/pith-number/GBR7TU3GDIUXDLQUNDXVUTLOV5/events.json","paper":"https://pith.science/paper/GBR7TU3G"},"agent_actions":{"view_html":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5","download_json":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5.json","view_paper":"https://pith.science/paper/GBR7TU3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.0615&json=true","fetch_graph":"https://pith.science/api/pith-number/GBR7TU3GDIUXDLQUNDXVUTLOV5/graph.json","fetch_events":"https://pith.science/api/pith-number/GBR7TU3GDIUXDLQUNDXVUTLOV5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5/action/storage_attestation","attest_author":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5/action/author_attestation","sign_citation":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5/action/citation_signature","submit_replication":"https://pith.science/pith/GBR7TU3GDIUXDLQUNDXVUTLOV5/action/replication_record"}},"created_at":"2026-05-18T04:00:02.783365+00:00","updated_at":"2026-05-18T04:00:02.783365+00:00"}