{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:U3N7FNCGBRBVTCSXHWXKCS6F5K","short_pith_number":"pith:U3N7FNCG","schema_version":"1.0","canonical_sha256":"a6dbf2b4460c43598a573daea14bc5ea90b10ecb4b21ca0f9397a5c945e61b86","source":{"kind":"arxiv","id":"1007.2994","version":2},"attestation_state":"computed","paper":{"title":"Trace formulae for perturbations of class $\\bs{\\bS_m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Alexei Aleksandrov, Vladimir Peller","submitted_at":"2010-07-18T12:07:10Z","abstract_excerpt":"We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class $\\bS_m$, where $m$ is a positive integer. In \\cite{PSS} a trace formula for operator Taylor polynomials was obtained. This formula includes the Livshits--Krein trace formula in the case $m=1$ and the Koplienko trace formula in the case $m=2$. We establish most general trace formulae in the case of perturbation of Schatten--von Neumann class $\\bS_m$. We also improve the trace formula obtained in \\cite{PSS} for operator Taylor polynomials and prove it for arbitrary functions "},"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":"1007.2994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-18T12:07:10Z","cross_cats_sorted":["math.CA","math.CV","math.SP"],"title_canon_sha256":"3231426fcc8f6b9a125faac32a0b1073042e24276f8efec20711a1ac37277f94","abstract_canon_sha256":"729d2e9e929ddeced47b8e26d82949faebbf3236fdbe97aa5079d10dbb296f54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:23.770868Z","signature_b64":"QJhF/vSWDNoPDNwj6YZY0wM1LIwX+j1NhgGFQPgU7MzlPVOkZ0sD3/u2XNZCywhiiw+ql88uWC1sax4toCqHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dbf2b4460c43598a573daea14bc5ea90b10ecb4b21ca0f9397a5c945e61b86","last_reissued_at":"2026-05-18T04:42:23.770431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:23.770431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trace formulae for perturbations of class $\\bs{\\bS_m}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.CV","math.SP"],"primary_cat":"math.FA","authors_text":"Alexei Aleksandrov, Vladimir Peller","submitted_at":"2010-07-18T12:07:10Z","abstract_excerpt":"We obtain general trace formulae in the case of perturbation of self-adjoint operators by self-adjoint operators of class $\\bS_m$, where $m$ is a positive integer. In \\cite{PSS} a trace formula for operator Taylor polynomials was obtained. This formula includes the Livshits--Krein trace formula in the case $m=1$ and the Koplienko trace formula in the case $m=2$. We establish most general trace formulae in the case of perturbation of Schatten--von Neumann class $\\bS_m$. We also improve the trace formula obtained in \\cite{PSS} for operator Taylor polynomials and prove it for arbitrary functions "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2994","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":"1007.2994","created_at":"2026-05-18T04:42:23.770497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.2994v2","created_at":"2026-05-18T04:42:23.770497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2994","created_at":"2026-05-18T04:42:23.770497+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3N7FNCGBRBV","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3N7FNCGBRBVTCSX","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3N7FNCG","created_at":"2026-05-18T12:26:15.391820+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/U3N7FNCGBRBVTCSXHWXKCS6F5K","json":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K.json","graph_json":"https://pith.science/api/pith-number/U3N7FNCGBRBVTCSXHWXKCS6F5K/graph.json","events_json":"https://pith.science/api/pith-number/U3N7FNCGBRBVTCSXHWXKCS6F5K/events.json","paper":"https://pith.science/paper/U3N7FNCG"},"agent_actions":{"view_html":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K","download_json":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K.json","view_paper":"https://pith.science/paper/U3N7FNCG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.2994&json=true","fetch_graph":"https://pith.science/api/pith-number/U3N7FNCGBRBVTCSXHWXKCS6F5K/graph.json","fetch_events":"https://pith.science/api/pith-number/U3N7FNCGBRBVTCSXHWXKCS6F5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K/action/storage_attestation","attest_author":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K/action/author_attestation","sign_citation":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K/action/citation_signature","submit_replication":"https://pith.science/pith/U3N7FNCGBRBVTCSXHWXKCS6F5K/action/replication_record"}},"created_at":"2026-05-18T04:42:23.770497+00:00","updated_at":"2026-05-18T04:42:23.770497+00:00"}