{"paper":{"title":"Characterization of BV functions on open domains: the Gaussian case and the general case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Davide Addona, Giorgio Menegatti, Michele Miranda Jr","submitted_at":"2019-02-26T12:25:37Z","abstract_excerpt":"We provide three different characterizations of the space $BV(O,\\gamma)$ of the functions of bounded variation with respect to a centred non-degenerate Gaussian measure $ \\gamma$ on open domains $O$ in Wiener spaces. Throughout these different characterizations we deduce a sufficient condition for belonging to $BV(O,\\gamma)$ by means of the Ornstein-Uhlenbeck semigroup and we provide an explicit formula for one-dimensional sections of functions of bounded variation. Finally, we apply our technique to Fomin differentiable probability measures $\\nu$ on a Hilbert space $X$, inferring a characteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09889","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"}