{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JMFEXNUHQURCQK4C3JWQ3EZP53","short_pith_number":"pith:JMFEXNUH","schema_version":"1.0","canonical_sha256":"4b0a4bb6878522282b82da6d0d932feedf30ce0b378da4fa13d4a9674895bb06","source":{"kind":"arxiv","id":"1503.05747","version":2},"attestation_state":"computed","paper":{"title":"Kato classes for L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"Karol Szczypkowski, Tomasz Grzywny","submitted_at":"2015-03-19T12:47:52Z","abstract_excerpt":"We prove that the definitions of the Kato class by the semigroup and by the resolvent of the L\\'{e}vy process on $\\mathbb{R}^d$ coincide if and only if 0 is not regular for {0}. If 0 is regular for {0} then we describe both classes in detail. We also give an analytic reformulation of these results by means of the characteristic (L\\'{e}vy-Khintchine) exponent of the process. The result applies to the time-dependent (non-autonomous) Kato class. As one of the consequences we obtain a simultaneous time-space smallness condition equivalent to the Kato class condition given by the semigroup."},"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":"1503.05747","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-19T12:47:52Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"ce8d136966cb415a41da4353b46065743d5ce5665ff729ccc21aeb7ff7c8c064","abstract_canon_sha256":"dad71007afbb816446681248a41098241d452bea0d7a0421f0ef2b598817fe42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:01.826946Z","signature_b64":"Jd9jb1RUc/DB+SNOSwNcRUX946lb/dXES+3nVGBlZY0zjFA33mHdOWRPDvylzvkXIEVx/p/2iGoTUZ+wm0f0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b0a4bb6878522282b82da6d0d932feedf30ce0b378da4fa13d4a9674895bb06","last_reissued_at":"2026-05-18T00:44:01.826179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:01.826179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kato classes for L\\'evy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.FA","authors_text":"Karol Szczypkowski, Tomasz Grzywny","submitted_at":"2015-03-19T12:47:52Z","abstract_excerpt":"We prove that the definitions of the Kato class by the semigroup and by the resolvent of the L\\'{e}vy process on $\\mathbb{R}^d$ coincide if and only if 0 is not regular for {0}. If 0 is regular for {0} then we describe both classes in detail. We also give an analytic reformulation of these results by means of the characteristic (L\\'{e}vy-Khintchine) exponent of the process. The result applies to the time-dependent (non-autonomous) Kato class. As one of the consequences we obtain a simultaneous time-space smallness condition equivalent to the Kato class condition given by the semigroup."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05747","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":"1503.05747","created_at":"2026-05-18T00:44:01.826304+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05747v2","created_at":"2026-05-18T00:44:01.826304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05747","created_at":"2026-05-18T00:44:01.826304+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMFEXNUHQURC","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMFEXNUHQURCQK4C","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMFEXNUH","created_at":"2026-05-18T12:29:27.538025+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/JMFEXNUHQURCQK4C3JWQ3EZP53","json":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53.json","graph_json":"https://pith.science/api/pith-number/JMFEXNUHQURCQK4C3JWQ3EZP53/graph.json","events_json":"https://pith.science/api/pith-number/JMFEXNUHQURCQK4C3JWQ3EZP53/events.json","paper":"https://pith.science/paper/JMFEXNUH"},"agent_actions":{"view_html":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53","download_json":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53.json","view_paper":"https://pith.science/paper/JMFEXNUH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05747&json=true","fetch_graph":"https://pith.science/api/pith-number/JMFEXNUHQURCQK4C3JWQ3EZP53/graph.json","fetch_events":"https://pith.science/api/pith-number/JMFEXNUHQURCQK4C3JWQ3EZP53/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53/action/storage_attestation","attest_author":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53/action/author_attestation","sign_citation":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53/action/citation_signature","submit_replication":"https://pith.science/pith/JMFEXNUHQURCQK4C3JWQ3EZP53/action/replication_record"}},"created_at":"2026-05-18T00:44:01.826304+00:00","updated_at":"2026-05-18T00:44:01.826304+00:00"}