{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GBR7TU3GDIUXDLQUNDXVUTLOV5","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":"d150d27c88f097a87dfc7a93fe4f4fdede704f827f79833331422285c1c4a8eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-04T16:31:01Z","title_canon_sha256":"79693dd504fc23233f8cf44a9ed443a80efa3453375a25c6a648ab70f8b99dee"},"schema_version":"1.0","source":{"id":"1104.0615","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0615","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0615v2","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0615","created_at":"2026-05-18T04:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"GBR7TU3GDIUX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"GBR7TU3GDIUXDLQU","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"GBR7TU3G","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:c2497a1b489b54e3da990aef4d348de67ac47adfa6f3f54c3d625dbcb4dbd816","target":"graph","created_at":"2026-05-18T04:00:02Z","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":"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","authors_text":"Wolfgang Erb","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-04T16:31:01Z","title":"An orthogonal polynomial analogue of the Landau-Pollak-Slepian time-frequency analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0615","kind":"arxiv","version":2},"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:f1a3c4314ce1d57f153692250569b84fad5944da6be87903c64626c75f777886","target":"record","created_at":"2026-05-18T04:00:02Z","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":"d150d27c88f097a87dfc7a93fe4f4fdede704f827f79833331422285c1c4a8eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-04-04T16:31:01Z","title_canon_sha256":"79693dd504fc23233f8cf44a9ed443a80efa3453375a25c6a648ab70f8b99dee"},"schema_version":"1.0","source":{"id":"1104.0615","kind":"arxiv","version":2}},"canonical_sha256":"3063f9d3661a2971ae1468ef5a4d6eaf421f8f45b2c46a2fbc498f8a5ecdd221","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3063f9d3661a2971ae1468ef5a4d6eaf421f8f45b2c46a2fbc498f8a5ecdd221","first_computed_at":"2026-05-18T04:00:02.783221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:02.783221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z+jCP7j1cPOIkMVSNE04/kSnTalQKjb4cFnAZ8xWSwsNtjU82oXZjYUOEOF7FGdP1AGn3qJfuq8+sAyNavJSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:02.784046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0615","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1a3c4314ce1d57f153692250569b84fad5944da6be87903c64626c75f777886","sha256:c2497a1b489b54e3da990aef4d348de67ac47adfa6f3f54c3d625dbcb4dbd816"],"state_sha256":"a249a161b11681a990759a71a54dc1056268b2cc9e63bc33ffb3d6405e224df8"}