{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KVSAAUDHJTNVB7KTTB2Y2OAQU6","short_pith_number":"pith:KVSAAUDH","schema_version":"1.0","canonical_sha256":"55640050674cdb50fd5398758d3810a782ff70ea117a162231ea9f9cb7be5f99","source":{"kind":"arxiv","id":"1904.07549","version":1},"attestation_state":"computed","paper":{"title":"Sylvester equations and polynomial separation of spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olavi Nevanlinna","submitted_at":"2019-04-16T09:26:56Z","abstract_excerpt":"Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ are well separated, either inside and outside of a circle or separated into different half planes. Much of the discussion is based on the following inclusion sets for the spectrum: $V_p(T)=\\{\\lambda \\in \\mathbb C \\ : \\ |p(\\lambda)| \\le \\|p(T)\\| \\}$ where $T$ is a bounded operator. We also give an explicit series expansion for the solution in te"},"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":"1904.07549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-16T09:26:56Z","cross_cats_sorted":[],"title_canon_sha256":"e71dc358bcf4a6906d03f4e1477684325f82cd064dce3facd32c456dc77b9c08","abstract_canon_sha256":"ecd753972694bcd345d2b27b7359e229ea83317f0df7137c53f9cb33f42c66b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:24.889454Z","signature_b64":"JA0/qw2W8ltVjsphmEGkpKQwcE500Ssi1kSCVzSoI7manRig5j7JynByEHeMUk89T5VzqC+ZAKfoFCxtCYcsDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55640050674cdb50fd5398758d3810a782ff70ea117a162231ea9f9cb7be5f99","last_reissued_at":"2026-05-17T23:48:24.888955Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:24.888955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sylvester equations and polynomial separation of spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olavi Nevanlinna","submitted_at":"2019-04-16T09:26:56Z","abstract_excerpt":"Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of $p(A)$ and $p(B)$ are well separated, either inside and outside of a circle or separated into different half planes. Much of the discussion is based on the following inclusion sets for the spectrum: $V_p(T)=\\{\\lambda \\in \\mathbb C \\ : \\ |p(\\lambda)| \\le \\|p(T)\\| \\}$ where $T$ is a bounded operator. We also give an explicit series expansion for the solution in te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07549","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":"1904.07549","created_at":"2026-05-17T23:48:24.889026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.07549v1","created_at":"2026-05-17T23:48:24.889026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07549","created_at":"2026-05-17T23:48:24.889026+00:00"},{"alias_kind":"pith_short_12","alias_value":"KVSAAUDHJTNV","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KVSAAUDHJTNVB7KT","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KVSAAUDH","created_at":"2026-05-18T12:33:21.387695+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/KVSAAUDHJTNVB7KTTB2Y2OAQU6","json":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6.json","graph_json":"https://pith.science/api/pith-number/KVSAAUDHJTNVB7KTTB2Y2OAQU6/graph.json","events_json":"https://pith.science/api/pith-number/KVSAAUDHJTNVB7KTTB2Y2OAQU6/events.json","paper":"https://pith.science/paper/KVSAAUDH"},"agent_actions":{"view_html":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6","download_json":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6.json","view_paper":"https://pith.science/paper/KVSAAUDH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.07549&json=true","fetch_graph":"https://pith.science/api/pith-number/KVSAAUDHJTNVB7KTTB2Y2OAQU6/graph.json","fetch_events":"https://pith.science/api/pith-number/KVSAAUDHJTNVB7KTTB2Y2OAQU6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6/action/storage_attestation","attest_author":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6/action/author_attestation","sign_citation":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6/action/citation_signature","submit_replication":"https://pith.science/pith/KVSAAUDHJTNVB7KTTB2Y2OAQU6/action/replication_record"}},"created_at":"2026-05-17T23:48:24.889026+00:00","updated_at":"2026-05-17T23:48:24.889026+00:00"}