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Ferrari","submitted_at":"2021-04-13T16:10:06Z","abstract_excerpt":"Let $X$ be a separable Banach space and let $Q:X^*\\rightarrow X$ be a linear, bounded, non-negative and symmetric operator and let $A:D(A)\\subseteq X\\rightarrow X$ be the infinitesimal generator of a strongly continuous semigroup of contractions on $X$. We consider the abstract Wiener space $(X,\\mu_\\infty,H_\\infty)$ where $\\mu_\\infty$ is a centred non-degenerate Gaussian measure on $X$ with covariance operator defined, at least formally, as \\begin{align*} Q_\\infty=\\int_0^{+\\infty} e^{sA}Qe^{sA^*}ds, \\end{align*} and $H_\\infty$ is the Cameron--Martin space associated to $\\mu_\\infty$.\n  Let $H$ "},"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":"2104.06327","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2021-04-13T16:10:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"62a6f85280f45e50905e56d4080db2b21b5a291356817b081f7f1c2a36726a55","abstract_canon_sha256":"4be49b247aa887072a7f73072587dd177df8fe56a46eac2dffa2757143ed0c99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:02:18.499481Z","signature_b64":"Vu7bniyhcR+BIRy4xMYWMWT++E5pJIXG3qpSkMHvGXc3co3YrR5ltSlZgWFQFMVn824AxOwwM6GGdncGMeMPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3818cac3836be5561dc996197451d95c72cfc32154d5a80ee9bd3ffd4c019e3","last_reissued_at":"2026-07-05T08:02:18.499052Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:02:18.499052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regarding the domain of non-symmetric and, possibly, degenerate Ornstein--Uhlenbeck operators in separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"D. Addona, G. Cappa, S. Ferrari","submitted_at":"2021-04-13T16:10:06Z","abstract_excerpt":"Let $X$ be a separable Banach space and let $Q:X^*\\rightarrow X$ be a linear, bounded, non-negative and symmetric operator and let $A:D(A)\\subseteq X\\rightarrow X$ be the infinitesimal generator of a strongly continuous semigroup of contractions on $X$. We consider the abstract Wiener space $(X,\\mu_\\infty,H_\\infty)$ where $\\mu_\\infty$ is a centred non-degenerate Gaussian measure on $X$ with covariance operator defined, at least formally, as \\begin{align*} Q_\\infty=\\int_0^{+\\infty} e^{sA}Qe^{sA^*}ds, \\end{align*} and $H_\\infty$ is the Cameron--Martin space associated to $\\mu_\\infty$.\n  Let $H$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.06327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2104.06327","created_at":"2026-07-05T08:02:18.499111+00:00"},{"alias_kind":"arxiv_version","alias_value":"2104.06327v1","created_at":"2026-07-05T08:02:18.499111+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.06327","created_at":"2026-07-05T08:02:18.499111+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OAYZLBYG27F","created_at":"2026-07-05T08:02:18.499111+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OAYZLBYG27FKYO4","created_at":"2026-07-05T08:02:18.499111+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OAYZLBY","created_at":"2026-07-05T08:02:18.499111+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/2OAYZLBYG27FKYO4TFQZORI5SX","json":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX.json","graph_json":"https://pith.science/api/pith-number/2OAYZLBYG27FKYO4TFQZORI5SX/graph.json","events_json":"https://pith.science/api/pith-number/2OAYZLBYG27FKYO4TFQZORI5SX/events.json","paper":"https://pith.science/paper/2OAYZLBY"},"agent_actions":{"view_html":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX","download_json":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX.json","view_paper":"https://pith.science/paper/2OAYZLBY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2104.06327&json=true","fetch_graph":"https://pith.science/api/pith-number/2OAYZLBYG27FKYO4TFQZORI5SX/graph.json","fetch_events":"https://pith.science/api/pith-number/2OAYZLBYG27FKYO4TFQZORI5SX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX/action/storage_attestation","attest_author":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX/action/author_attestation","sign_citation":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX/action/citation_signature","submit_replication":"https://pith.science/pith/2OAYZLBYG27FKYO4TFQZORI5SX/action/replication_record"}},"created_at":"2026-07-05T08:02:18.499111+00:00","updated_at":"2026-07-05T08:02:18.499111+00:00"}