{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BAXMLGEVVUPTIH3AKELUEAR3KH","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":"6e0712b20a9eb559be5c209f6adcbf27b717db8e4023627bfbdef2f6424567e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-29T11:08:39Z","title_canon_sha256":"71860f7fa953940cbc6bbc7323d6666c50453274ef8b08a63ba0a0a9c90c6462"},"schema_version":"1.0","source":{"id":"1309.7574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7574","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7574v2","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7574","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"BAXMLGEVVUPT","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BAXMLGEVVUPTIH3A","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BAXMLGEV","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:673d69a0e699ec66e98d716646dae167cb8c89366d1fa56102d3c4cbfc7e8e7a","target":"graph","created_at":"2026-05-18T03:00:00Z","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":"Toeplitz plus Hankel operators $T(a)+H(b)$, $a,b\\in L^\\infty$ acting on the classical Hardy spaces $H^p, 1<p<\\infty$, are studied. If the generating functions $a$ and $b$ satisfy the so-called matching condition $a(t) a(1/t)=b(t) b(1/t)$, an effective description of the structure of the kernel and cokernel of the corresponding operator is given. The results depend on the behaviour of two auxiliary scalar Toeplitz operators, and if the generating functions $a$ and $b$ are piecewise continuous, more detailed results are obtained.","authors_text":"Bernd Silbermann, Victor D. Didenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-29T11:08:39Z","title":"Structure of Kernels and Cokernels of Toeplitz plus Hankel Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7574","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":"sha256:0c332c81478904817b847c1adaa51a70694244feb0b32852196325e8cbae1860","target":"record","created_at":"2026-05-18T03:00:00Z","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":"6e0712b20a9eb559be5c209f6adcbf27b717db8e4023627bfbdef2f6424567e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-29T11:08:39Z","title_canon_sha256":"71860f7fa953940cbc6bbc7323d6666c50453274ef8b08a63ba0a0a9c90c6462"},"schema_version":"1.0","source":{"id":"1309.7574","kind":"arxiv","version":2}},"canonical_sha256":"082ec59895ad1f341f60511742023b51d20cb45d3eb7351d30730f9625f194b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"082ec59895ad1f341f60511742023b51d20cb45d3eb7351d30730f9625f194b9","first_computed_at":"2026-05-18T03:00:00.577425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:00.577425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DCs4FYxCgB7FwvbYWPBA1lblzcdpo/1XDzZ0XeJXTwge/66nLUfxwuH7zDG79xX9T9dKVfoh5AQxd+l5LF63DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:00.578204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c332c81478904817b847c1adaa51a70694244feb0b32852196325e8cbae1860","sha256:673d69a0e699ec66e98d716646dae167cb8c89366d1fa56102d3c4cbfc7e8e7a"],"state_sha256":"6f293d31607cf5fefcfb029e279aeb5870e9cfdf07dc8e721b9d8997f9c2f04b"}