{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:2S7UEKX2J6YDSRD4PBG2DLXSBU","short_pith_number":"pith:2S7UEKX2","schema_version":"1.0","canonical_sha256":"d4bf422afa4fb039447c784da1aef20d019e7c827992774e8fca29ec47e7161b","source":{"kind":"arxiv","id":"0807.1045","version":2},"attestation_state":"computed","paper":{"title":"$AC(\\sigma)$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Brenden Ashton, Ian Doust","submitted_at":"2008-07-07T15:42:55Z","abstract_excerpt":"In this paper we present a new extension of the theory of well-bounded operators to cover operators with complex spectrum. In previous work a new concept of the class of absolutely continuous functions on a nonempty compact subset $\\sigma$ of the plane, denoted $AC(\\sigma)$, was introduced. An $\\AC(\\sigma)$ operator is one which admits a functional calculus for this algebra of functions. The class of $AC(\\sigma)$ operators includes all of the well-bounded operators and trigonometrically well-bounded operators, as well as all scalar-type spectral operators, but is strictly smaller than Berkson "},"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":"0807.1045","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2008-07-07T15:42:55Z","cross_cats_sorted":[],"title_canon_sha256":"e30d307b1eb143925716c5dcb620b82e48e12f772427f2a398dfe29a9285c323","abstract_canon_sha256":"fad4056970427da78885315388c362d5c38f510e820e93436eb88702fb7b3fe2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:32.312595Z","signature_b64":"cod/LwhsQnlwKj8v8w8mnRupxEM5H7ixz5p/6Z7lyPGrvUKruTyMraAId15SkzXzBbqneaSG4+Z4NcaPVtrxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4bf422afa4fb039447c784da1aef20d019e7c827992774e8fca29ec47e7161b","last_reissued_at":"2026-05-18T03:07:32.311987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:32.311987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$AC(\\sigma)$ operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Brenden Ashton, Ian Doust","submitted_at":"2008-07-07T15:42:55Z","abstract_excerpt":"In this paper we present a new extension of the theory of well-bounded operators to cover operators with complex spectrum. In previous work a new concept of the class of absolutely continuous functions on a nonempty compact subset $\\sigma$ of the plane, denoted $AC(\\sigma)$, was introduced. An $\\AC(\\sigma)$ operator is one which admits a functional calculus for this algebra of functions. The class of $AC(\\sigma)$ operators includes all of the well-bounded operators and trigonometrically well-bounded operators, as well as all scalar-type spectral operators, but is strictly smaller than Berkson "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1045","kind":"arxiv","version":2},"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":"0807.1045","created_at":"2026-05-18T03:07:32.312080+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.1045v2","created_at":"2026-05-18T03:07:32.312080+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1045","created_at":"2026-05-18T03:07:32.312080+00:00"},{"alias_kind":"pith_short_12","alias_value":"2S7UEKX2J6YD","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"2S7UEKX2J6YDSRD4","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"2S7UEKX2","created_at":"2026-05-18T12:25:56.245647+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/2S7UEKX2J6YDSRD4PBG2DLXSBU","json":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU.json","graph_json":"https://pith.science/api/pith-number/2S7UEKX2J6YDSRD4PBG2DLXSBU/graph.json","events_json":"https://pith.science/api/pith-number/2S7UEKX2J6YDSRD4PBG2DLXSBU/events.json","paper":"https://pith.science/paper/2S7UEKX2"},"agent_actions":{"view_html":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU","download_json":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU.json","view_paper":"https://pith.science/paper/2S7UEKX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.1045&json=true","fetch_graph":"https://pith.science/api/pith-number/2S7UEKX2J6YDSRD4PBG2DLXSBU/graph.json","fetch_events":"https://pith.science/api/pith-number/2S7UEKX2J6YDSRD4PBG2DLXSBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU/action/storage_attestation","attest_author":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU/action/author_attestation","sign_citation":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU/action/citation_signature","submit_replication":"https://pith.science/pith/2S7UEKX2J6YDSRD4PBG2DLXSBU/action/replication_record"}},"created_at":"2026-05-18T03:07:32.312080+00:00","updated_at":"2026-05-18T03:07:32.312080+00:00"}