{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MTFLBMH5KLER7RKBYT4KVTKUVY","short_pith_number":"pith:MTFLBMH5","schema_version":"1.0","canonical_sha256":"64cab0b0fd52c91fc541c4f8aacd54ae0ede1849a88383145894afc2fd8bf7c2","source":{"kind":"arxiv","id":"1404.6742","version":1},"attestation_state":"computed","paper":{"title":"Quasi-Carleman operators and their spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"D. R. Yafaev","submitted_at":"2014-04-27T12:06:03Z","abstract_excerpt":"The Carleman operator is defined as integral operator with kernel $(t+s)^{-1}$ in the space $L^2 ({\\Bbb R}_{+}) $. This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint Hankel operators (we call them quasi-Carleman operators) generalizing the Carleman operator in various directions. We find explicit formulas for the total number of negative eigenvalues of quasi-Carleman operators and, in particular, necessary and sufficient conditions for their positivity. Our approach relies on the concepts of the sigma-function and of th"},"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":"1404.6742","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-27T12:06:03Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"1e7248e83bc405f5de069c59399c20c5aaa2ed25997c85dc1def62d4683acbef","abstract_canon_sha256":"ecc3c83dab560cedd1c6d1f4b3a0d2dd913464a54bed81e0e14efb371256da8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:06.105834Z","signature_b64":"hZvQD5f3S6UWYfraSTIV58HYpxcuZTc3PapdCFDp/SsOPzVP3Yyk1sE4C421CgqBriA2p+mFkP2fUCxPA0jfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64cab0b0fd52c91fc541c4f8aacd54ae0ede1849a88383145894afc2fd8bf7c2","last_reissued_at":"2026-05-18T02:53:06.105221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:06.105221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quasi-Carleman operators and their spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"D. R. Yafaev","submitted_at":"2014-04-27T12:06:03Z","abstract_excerpt":"The Carleman operator is defined as integral operator with kernel $(t+s)^{-1}$ in the space $L^2 ({\\Bbb R}_{+}) $. This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint Hankel operators (we call them quasi-Carleman operators) generalizing the Carleman operator in various directions. We find explicit formulas for the total number of negative eigenvalues of quasi-Carleman operators and, in particular, necessary and sufficient conditions for their positivity. Our approach relies on the concepts of the sigma-function and of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6742","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":"1404.6742","created_at":"2026-05-18T02:53:06.105333+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6742v1","created_at":"2026-05-18T02:53:06.105333+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6742","created_at":"2026-05-18T02:53:06.105333+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTFLBMH5KLER","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTFLBMH5KLER7RKB","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTFLBMH5","created_at":"2026-05-18T12:28:38.356838+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/MTFLBMH5KLER7RKBYT4KVTKUVY","json":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY.json","graph_json":"https://pith.science/api/pith-number/MTFLBMH5KLER7RKBYT4KVTKUVY/graph.json","events_json":"https://pith.science/api/pith-number/MTFLBMH5KLER7RKBYT4KVTKUVY/events.json","paper":"https://pith.science/paper/MTFLBMH5"},"agent_actions":{"view_html":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY","download_json":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY.json","view_paper":"https://pith.science/paper/MTFLBMH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6742&json=true","fetch_graph":"https://pith.science/api/pith-number/MTFLBMH5KLER7RKBYT4KVTKUVY/graph.json","fetch_events":"https://pith.science/api/pith-number/MTFLBMH5KLER7RKBYT4KVTKUVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY/action/storage_attestation","attest_author":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY/action/author_attestation","sign_citation":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY/action/citation_signature","submit_replication":"https://pith.science/pith/MTFLBMH5KLER7RKBYT4KVTKUVY/action/replication_record"}},"created_at":"2026-05-18T02:53:06.105333+00:00","updated_at":"2026-05-18T02:53:06.105333+00:00"}