{"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"}