{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5GUU6RYTR5QJXBOPQC2ROYIBR3","short_pith_number":"pith:5GUU6RYT","schema_version":"1.0","canonical_sha256":"e9a94f47138f609b85cf80b51761018eea680f17290148b84c07ea6ae51aaeab","source":{"kind":"arxiv","id":"1501.04271","version":1},"attestation_state":"computed","paper":{"title":"Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernd Silbermann, Victor D. Didenko","submitted_at":"2015-01-18T08:12:16Z","abstract_excerpt":"Generalized Toeplitz plus Hankel operators $T(a)+H_{\\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\\alpha$ changing the orientation of the unit circle $\\mathbb{T}$ are considered on the Hardy spaces $H^p(\\mathbb{T})$, $1<p<\\infty$. If the functions $a,b\\in L^\\infty(\\mathbb{T})$ and satisfy the condition\n  $$ a(t) a(\\alpha(t))=b(t) b(\\alpha(t)),\\quad t\\in \\mathbb{T}, $$ the defect numbers of the operators $T(a)+H_{\\alpha}(b)$ are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given."},"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":"1501.04271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-01-18T08:12:16Z","cross_cats_sorted":[],"title_canon_sha256":"330e6a19ffda13b029190111dcc8df62e05617aef6ccfab550fc0ae9565e26b3","abstract_canon_sha256":"8ed9b0f1b00d5ccdf000c0b37fba436e9e592de3361ad63bd1f1e9aa342ddc3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:09.544399Z","signature_b64":"N0CcO9zEmo7/bl8ingY0/Wafmg38pc4M7KOm/SyxJ1P9VbpOgs9g3rNz6LDGx674SkBSBViDfnG2zpfPOgCyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9a94f47138f609b85cf80b51761018eea680f17290148b84c07ea6ae51aaeab","last_reissued_at":"2026-05-18T02:29:09.543740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:09.543740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Toeplitz plus Hankel operators: kernel structure and defect numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bernd Silbermann, Victor D. Didenko","submitted_at":"2015-01-18T08:12:16Z","abstract_excerpt":"Generalized Toeplitz plus Hankel operators $T(a)+H_{\\alpha}(b)$ generated by functions $a,b$ and a linear fractional Carleman shift $\\alpha$ changing the orientation of the unit circle $\\mathbb{T}$ are considered on the Hardy spaces $H^p(\\mathbb{T})$, $1<p<\\infty$. If the functions $a,b\\in L^\\infty(\\mathbb{T})$ and satisfy the condition\n  $$ a(t) a(\\alpha(t))=b(t) b(\\alpha(t)),\\quad t\\in \\mathbb{T}, $$ the defect numbers of the operators $T(a)+H_{\\alpha}(b)$ are established and an explicit description of the structure of the kernels and cokernels of the operators mentioned is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04271","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":"1501.04271","created_at":"2026-05-18T02:29:09.543837+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04271v1","created_at":"2026-05-18T02:29:09.543837+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04271","created_at":"2026-05-18T02:29:09.543837+00:00"},{"alias_kind":"pith_short_12","alias_value":"5GUU6RYTR5QJ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5GUU6RYTR5QJXBOP","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5GUU6RYT","created_at":"2026-05-18T12:29:05.191682+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/5GUU6RYTR5QJXBOPQC2ROYIBR3","json":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3.json","graph_json":"https://pith.science/api/pith-number/5GUU6RYTR5QJXBOPQC2ROYIBR3/graph.json","events_json":"https://pith.science/api/pith-number/5GUU6RYTR5QJXBOPQC2ROYIBR3/events.json","paper":"https://pith.science/paper/5GUU6RYT"},"agent_actions":{"view_html":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3","download_json":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3.json","view_paper":"https://pith.science/paper/5GUU6RYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04271&json=true","fetch_graph":"https://pith.science/api/pith-number/5GUU6RYTR5QJXBOPQC2ROYIBR3/graph.json","fetch_events":"https://pith.science/api/pith-number/5GUU6RYTR5QJXBOPQC2ROYIBR3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3/action/storage_attestation","attest_author":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3/action/author_attestation","sign_citation":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3/action/citation_signature","submit_replication":"https://pith.science/pith/5GUU6RYTR5QJXBOPQC2ROYIBR3/action/replication_record"}},"created_at":"2026-05-18T02:29:09.543837+00:00","updated_at":"2026-05-18T02:29:09.543837+00:00"}