{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XOXCFGX7XG3CGHZRBJ7AMXSWLX","short_pith_number":"pith:XOXCFGX7","schema_version":"1.0","canonical_sha256":"bbae229affb9b6231f310a7e065e565dd626439212cb19d7c719761686ee0c3a","source":{"kind":"arxiv","id":"1904.13199","version":1},"attestation_state":"computed","paper":{"title":"On infinite Jacobi matrices with a trace class resolvent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek","submitted_at":"2019-04-30T12:48:47Z","abstract_excerpt":"Let $\\{\\hat{P}_{n}(x)\\}$ be an orthonormal polynomial sequence and denote by $\\{w_{n}(x)\\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\\{\\hat{P}_{n}(x)\\}$ is determinate and denote by $J$ the corresponding Jacobi matrix operator on $\\ell^{2}$. We show that if $J$ is positive definite and $J^{-1}$ belongs to the trace class then the series on the right-hand side of the defining equation \\[ \\mathfrak{F}(z):=1-z\\sum_{n=0}^{\\infty}w_{n}(0)\\hat{P}_{n}(z) \\] converges locally uniformly on $\\mathbb{C}$ and it holds true that $\\mathfrak{F}(z)=\\pr"},"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":"1904.13199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2019-04-30T12:48:47Z","cross_cats_sorted":[],"title_canon_sha256":"10ac5b6023517a7c2ce2e31cd54fee1ae9c5194179320420bd23da5fedb862bf","abstract_canon_sha256":"e329c7d966896615f5262082155ce6f7e2336a1d4fab0ccb5abcf0ef45202067"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:21.955661Z","signature_b64":"L2YOGQTz9a+UQBKWGbLnW8mctSNiJQqBpT8t83gIOh01NEJqSNsxbxXJJM0zlBQ+lpS4LblH7OBXm/hViTDfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbae229affb9b6231f310a7e065e565dd626439212cb19d7c719761686ee0c3a","last_reissued_at":"2026-05-17T23:47:21.955256Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:21.955256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On infinite Jacobi matrices with a trace class resolvent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Pavel Stovicek","submitted_at":"2019-04-30T12:48:47Z","abstract_excerpt":"Let $\\{\\hat{P}_{n}(x)\\}$ be an orthonormal polynomial sequence and denote by $\\{w_{n}(x)\\}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for $\\{\\hat{P}_{n}(x)\\}$ is determinate and denote by $J$ the corresponding Jacobi matrix operator on $\\ell^{2}$. We show that if $J$ is positive definite and $J^{-1}$ belongs to the trace class then the series on the right-hand side of the defining equation \\[ \\mathfrak{F}(z):=1-z\\sum_{n=0}^{\\infty}w_{n}(0)\\hat{P}_{n}(z) \\] converges locally uniformly on $\\mathbb{C}$ and it holds true that $\\mathfrak{F}(z)=\\pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.13199","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":"1904.13199","created_at":"2026-05-17T23:47:21.955325+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.13199v1","created_at":"2026-05-17T23:47:21.955325+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.13199","created_at":"2026-05-17T23:47:21.955325+00:00"},{"alias_kind":"pith_short_12","alias_value":"XOXCFGX7XG3C","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"XOXCFGX7XG3CGHZR","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"XOXCFGX7","created_at":"2026-05-18T12:33:33.725879+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/XOXCFGX7XG3CGHZRBJ7AMXSWLX","json":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX.json","graph_json":"https://pith.science/api/pith-number/XOXCFGX7XG3CGHZRBJ7AMXSWLX/graph.json","events_json":"https://pith.science/api/pith-number/XOXCFGX7XG3CGHZRBJ7AMXSWLX/events.json","paper":"https://pith.science/paper/XOXCFGX7"},"agent_actions":{"view_html":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX","download_json":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX.json","view_paper":"https://pith.science/paper/XOXCFGX7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.13199&json=true","fetch_graph":"https://pith.science/api/pith-number/XOXCFGX7XG3CGHZRBJ7AMXSWLX/graph.json","fetch_events":"https://pith.science/api/pith-number/XOXCFGX7XG3CGHZRBJ7AMXSWLX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX/action/storage_attestation","attest_author":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX/action/author_attestation","sign_citation":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX/action/citation_signature","submit_replication":"https://pith.science/pith/XOXCFGX7XG3CGHZRBJ7AMXSWLX/action/replication_record"}},"created_at":"2026-05-17T23:47:21.955325+00:00","updated_at":"2026-05-17T23:47:21.955325+00:00"}