{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:TXYYJ2PRO3GYFKSGB36AX22PSH","short_pith_number":"pith:TXYYJ2PR","schema_version":"1.0","canonical_sha256":"9df184e9f176cd82aa460efc0beb4f91c6f23fef787a0e0b33c48fbb704cff8e","source":{"kind":"arxiv","id":"1411.5866","version":2},"attestation_state":"computed","paper":{"title":"Duality between Eigenfunctions and Eigendistributions of Ruelle and Koopman operators via an integral kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Paolo Giulietti, Vincent Pit","submitted_at":"2014-11-21T13:25:46Z","abstract_excerpt":"We consider the classical dynamics given by a one sided shift on the Bernoulli space of $d$ symbols. We study, on the space of H\\\"older functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows that for any isolated eigenvalue, the eigendistributions of such Ruelle operator are dual to eigenvectors of a Ruelle operator with a conjugate potential. We also show that the eigenfunctions and eigendistributions of the Koopman operator satisfy a similar relationship. To show such results we employ an integral kernel technique, where the kernel used is the"},"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":"1411.5866","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-21T13:25:46Z","cross_cats_sorted":["cond-mat.stat-mech","math.PR"],"title_canon_sha256":"b4b65731d95557c51fe9b7a429f5825b14f33c72a53ad583b440bd42cf163998","abstract_canon_sha256":"75569907dec9a94a1b4b38cede0f958c8576b1421fcb2d10a2d836c32bf6d313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:38.211907Z","signature_b64":"+kl8Ay03+p2HdfRy/3dZRnSz6kg2shDxeugZoWq+tJ2a4hVCTpwyob7mzixSn21xYAX0Ncy9hDI08ng1AkAJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9df184e9f176cd82aa460efc0beb4f91c6f23fef787a0e0b33c48fbb704cff8e","last_reissued_at":"2026-05-18T01:59:38.211132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:38.211132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Duality between Eigenfunctions and Eigendistributions of Ruelle and Koopman operators via an integral kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Paolo Giulietti, Vincent Pit","submitted_at":"2014-11-21T13:25:46Z","abstract_excerpt":"We consider the classical dynamics given by a one sided shift on the Bernoulli space of $d$ symbols. We study, on the space of H\\\"older functions, the eigendistributions of the Ruelle operator with a given potential. Our main theorem shows that for any isolated eigenvalue, the eigendistributions of such Ruelle operator are dual to eigenvectors of a Ruelle operator with a conjugate potential. We also show that the eigenfunctions and eigendistributions of the Koopman operator satisfy a similar relationship. To show such results we employ an integral kernel technique, where the kernel used is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5866","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":"1411.5866","created_at":"2026-05-18T01:59:38.211235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.5866v2","created_at":"2026-05-18T01:59:38.211235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5866","created_at":"2026-05-18T01:59:38.211235+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXYYJ2PRO3GY","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXYYJ2PRO3GYFKSG","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXYYJ2PR","created_at":"2026-05-18T12:28:52.271510+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/TXYYJ2PRO3GYFKSGB36AX22PSH","json":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH.json","graph_json":"https://pith.science/api/pith-number/TXYYJ2PRO3GYFKSGB36AX22PSH/graph.json","events_json":"https://pith.science/api/pith-number/TXYYJ2PRO3GYFKSGB36AX22PSH/events.json","paper":"https://pith.science/paper/TXYYJ2PR"},"agent_actions":{"view_html":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH","download_json":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH.json","view_paper":"https://pith.science/paper/TXYYJ2PR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.5866&json=true","fetch_graph":"https://pith.science/api/pith-number/TXYYJ2PRO3GYFKSGB36AX22PSH/graph.json","fetch_events":"https://pith.science/api/pith-number/TXYYJ2PRO3GYFKSGB36AX22PSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH/action/storage_attestation","attest_author":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH/action/author_attestation","sign_citation":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH/action/citation_signature","submit_replication":"https://pith.science/pith/TXYYJ2PRO3GYFKSGB36AX22PSH/action/replication_record"}},"created_at":"2026-05-18T01:59:38.211235+00:00","updated_at":"2026-05-18T01:59:38.211235+00:00"}