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We present a method of determining the proper dissipative extensions $\\widehat{A}$ of this dual pair, i.e. $A\\subset \\widehat{A}\\subset\\widetilde{A}^*$ provided that $\\mathcal{D}(A)\\cap\\mathcal{D}(\\widetilde{A})$ is dense in $\\mathcal{H}$.\n  Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are"},"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":"1603.08192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-27T09:12:27Z","cross_cats_sorted":[],"title_canon_sha256":"bad94cc5fa2a71356915e74d5f1397fb18799a0227d0a5dab40408276e28d6df","abstract_canon_sha256":"e0ded23ef669f75222c7d954c9fa43294425a0695c6a2b50c0daffc29f4647dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:12.979977Z","signature_b64":"Lm79BObcyHJIbygJMnAwgV1NU+vGm8LTnKEKZzDZ5RZN14MZc2pAV+ttzTeOopkeEueD8s7JVZpjYzRTuGF1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"005afed1058f601e86d7bf1cf0bf0ba49929683c6b62ca151d5c6e5f7ce2b00e","last_reissued_at":"2026-05-18T01:18:12.979378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:12.979378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Proper Dissipative Extensions of a Dual Pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christoph Fischbacher, Ian Wood, Sergey Naboko","submitted_at":"2016-03-27T09:12:27Z","abstract_excerpt":"Let $A$ and $(-\\widetilde{A})$ be dissipative operators on a Hilbert space $\\mathcal{H}$ and let $(A,\\widetilde{A})$ form a dual pair, i.e. $A\\subset\\widetilde{A}^*$, resp.\\ $\\widetilde{A}\\subset A^*$. We present a method of determining the proper dissipative extensions $\\widehat{A}$ of this dual pair, i.e. $A\\subset \\widehat{A}\\subset\\widetilde{A}^*$ provided that $\\mathcal{D}(A)\\cap\\mathcal{D}(\\widetilde{A})$ is dense in $\\mathcal{H}$.\n  Applications to symmetric operators, symmetric operators perturbed by a relatively bounded dissipative operator and more singular differential operators are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08192","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":"1603.08192","created_at":"2026-05-18T01:18:12.979481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08192v1","created_at":"2026-05-18T01:18:12.979481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08192","created_at":"2026-05-18T01:18:12.979481+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABNP5UIFR5QB","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABNP5UIFR5QB5BWX","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABNP5UIF","created_at":"2026-05-18T12:30:07.202191+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/ABNP5UIFR5QB5BWXX4OPBPYLUS","json":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS.json","graph_json":"https://pith.science/api/pith-number/ABNP5UIFR5QB5BWXX4OPBPYLUS/graph.json","events_json":"https://pith.science/api/pith-number/ABNP5UIFR5QB5BWXX4OPBPYLUS/events.json","paper":"https://pith.science/paper/ABNP5UIF"},"agent_actions":{"view_html":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS","download_json":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS.json","view_paper":"https://pith.science/paper/ABNP5UIF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08192&json=true","fetch_graph":"https://pith.science/api/pith-number/ABNP5UIFR5QB5BWXX4OPBPYLUS/graph.json","fetch_events":"https://pith.science/api/pith-number/ABNP5UIFR5QB5BWXX4OPBPYLUS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS/action/storage_attestation","attest_author":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS/action/author_attestation","sign_citation":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS/action/citation_signature","submit_replication":"https://pith.science/pith/ABNP5UIFR5QB5BWXX4OPBPYLUS/action/replication_record"}},"created_at":"2026-05-18T01:18:12.979481+00:00","updated_at":"2026-05-18T01:18:12.979481+00:00"}